{
  "title": "Area Ratio of Similar Triangles - Grade 10 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "If two triangles are similar with similarity ratio 2:3, what is the ratio of their areas?", "options": {"A": "2:3", "B": "3:2", "C": "4:9", "D": "9:4"}, "correct_answer": "C"},
    {"id": 2, "difficulty": "easy", "question": "The ratio of areas of two similar triangles is 9:16. What is the ratio of their corresponding sides?", "options": {"A": "3:4", "B": "4:3", "C": "9:16", "D": "81:256"}, "correct_answer": "A"},
    {"id": 3, "difficulty": "easy", "question": "If ΔABC ~ ΔDEF and area(ΔABC)=25 cm², area(ΔDEF)=100 cm², what is the ratio of their corresponding sides?", "options": {"A": "1:2", "B": "1:4", "C": "2:1", "D": "5:10"}, "correct_answer": "A"},
    {"id": 4, "difficulty": "easy", "question": "Two similar triangles have sides in ratio 5:7. What is the ratio of their areas?", "options": {"A": "5:7", "B": "25:49", "C": "7:5", "D": "49:25"}, "correct_answer": "B"},
    {"id": 5, "difficulty": "easy", "question": "If the areas of two similar triangles are 64 cm² and 144 cm², what is the ratio of their corresponding sides?", "options": {"A": "8:12", "B": "2:3", "C": "4:9", "D": "64:144"}, "correct_answer": "A"},
    {"id": 6, "difficulty": "easy", "question": "The sides of two similar triangles are in ratio 3:5. If area of smaller triangle is 27 cm², what is area of larger triangle?", "options": {"A": "45 cm²", "B": "75 cm²", "C": "125 cm²", "D": "81 cm²"}, "correct_answer": "B"},
    {"id": 7, "difficulty": "easy", "question": "If area ratio of two similar triangles is 1:4, what is the ratio of their corresponding sides?", "options": {"A": "1:2", "B": "1:4", "C": "2:1", "D": "4:1"}, "correct_answer": "A"},
    {"id": 8, "difficulty": "easy", "question": "ΔPQR ~ ΔXYZ. If PQ:XY = 2:3 and area of ΔPQR = 20 cm², what is area of ΔXYZ?", "options": {"A": "30 cm²", "B": "40 cm²", "C": "45 cm²", "D": "60 cm²"}, "correct_answer": "C"},
    {"id": 9, "difficulty": "easy", "question": "Two triangles have areas 16 cm² and 36 cm². If they are similar, what is the ratio of their corresponding sides?", "options": {"A": "16:36", "B": "4:6", "C": "2:3", "D": "8:18"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "If similarity ratio is 4:7, what is the area ratio?", "options": {"A": "4:7", "B": "16:49", "C": "7:4", "D": "49:16"}, "correct_answer": "B"},
    {"id": 11, "difficulty": "easy", "question": "The area of ΔABC is 48 cm² and ΔDEF ~ ΔABC with sides ratio 1:2. What is area of ΔDEF?", "options": {"A": "12 cm²", "B": "24 cm²", "C": "96 cm²", "D": "192 cm²"}, "correct_answer": "D"},
    {"id": 12, "difficulty": "easy", "question": "Two similar triangles have perimeters 18 cm and 24 cm. What is the ratio of their areas?", "options": {"A": "18:24", "B": "3:4", "C": "9:16", "D": "81:144"}, "correct_answer": "C"},
    {"id": 13, "difficulty": "easy", "question": "If side ratio = 5:8, then area ratio = ?", "options": {"A": "5:8", "B": "25:64", "C": "10:16", "D": "50:128"}, "correct_answer": "B"},
    {"id": 14, "difficulty": "easy", "question": "Area of ΔMNO = 75 cm², ΔPQR ~ ΔMNO with side ratio 2:5. Area of ΔPQR = ?", "options": {"A": "30 cm²", "B": "120 cm²", "C": "187.5 cm²", "D": "468.75 cm²"}, "correct_answer": "D"},
    {"id": 15, "difficulty": "easy", "question": "The ratio of areas of two similar triangles is 25:36. Their corresponding altitudes are in ratio?", "options": {"A": "25:36", "B": "5:6", "C": "6:5", "D": "625:1296"}, "correct_answer": "B"},
    {"id": 16, "difficulty": "easy", "question": "If two triangles are similar and one side is twice the corresponding side, area of larger triangle is ___ times smaller.", "options": {"A": "2", "B": "3", "C": "4", "D": "8"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "ΔABC ~ ΔDEF. AB = 6 cm, DE = 9 cm, area(ΔABC)=54 cm². Area(ΔDEF)=?", "options": {"A": "81 cm²", "B": "121.5 cm²", "C": "162 cm²", "D": "243 cm²"}, "correct_answer": "B"},
    {"id": 18, "difficulty": "easy", "question": "The areas of two similar triangles are 100 cm² and 225 cm². Their similarity ratio is?", "options": {"A": "10:15", "B": "2:3", "C": "4:9", "D": "100:225"}, "correct_answer": "A"},
    {"id": 19, "difficulty": "easy", "question": "If area ratio is 49:81, then side ratio is?", "options": {"A": "49:81", "B": "7:9", "C": "9:7", "D": "2401:6561"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "Two similar triangles have corresponding medians in ratio 3:4. Their areas are in ratio?", "options": {"A": "3:4", "B": "6:8", "C": "9:16", "D": "27:64"}, "correct_answer": "C"},
    
    {"id": 21, "difficulty": "medium", "question": "ΔABC ~ ΔPQR. Area(ΔABC)=36 cm², BC=6 cm, QR=9 cm. Find area(ΔPQR).", "options": {"A": "54 cm²", "B": "81 cm²", "C": "72 cm²", "D": "90 cm²"}, "correct_answer": "B"},
    {"id": 22, "difficulty": "medium", "question": "Two similar triangles have areas 121 cm² and 169 cm². If a side of smaller triangle is 11 cm, find corresponding side of larger triangle.", "options": {"A": "12 cm", "B": "13 cm", "C": "14 cm", "D": "15 cm"}, "correct_answer": "B"},
    {"id": 23, "difficulty": "medium", "question": "The areas of two similar triangles are in ratio 16:25. If one side of first triangle is 8 cm, find corresponding side of second triangle.", "options": {"A": "10 cm", "B": "12.5 cm", "C": "9 cm", "D": "11 cm"}, "correct_answer": "A"},
    {"id": 24, "difficulty": "medium", "question": "ΔLMN ~ ΔXYZ. Area(LMN)=64 cm², area(XYZ)=144 cm². If LM=8 cm, find XY.", "options": {"A": "9 cm", "B": "10 cm", "C": "11 cm", "D": "12 cm"}, "correct_answer": "D"},
    {"id": 25, "difficulty": "medium", "question": "Two similar triangles have perimeters 30 cm and 45 cm. If area of smaller is 60 cm², find area of larger.", "options": {"A": "90 cm²", "B": "120 cm²", "C": "135 cm²", "D": "150 cm²"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "The ratio of corresponding altitudes of two similar triangles is 2:5. Find ratio of their areas.", "options": {"A": "2:5", "B": "4:25", "C": "5:2", "D": "25:4"}, "correct_answer": "B"},
    {"id": 27, "difficulty": "medium", "question": "ΔABC ~ ΔDEF. AB=5 cm, DE=7.5 cm. If altitude from A to BC=4 cm, find altitude from D to EF.", "options": {"A": "5 cm", "B": "6 cm", "C": "7 cm", "D": "8 cm"}, "correct_answer": "B"},
    {"id": 28, "difficulty": "medium", "question": "Two similar triangles have areas 81 cm² and 144 cm². If perimeter of first is 27 cm, find perimeter of second.", "options": {"A": "36 cm", "B": "42 cm", "C": "45 cm", "D": "48 cm"}, "correct_answer": "A"},
    {"id": 29, "difficulty": "medium", "question": "In ΔABC and ΔPQR, AB/PQ = BC/QR = 3/4. If area(ΔABC)=108 cm², find area(ΔPQR).", "options": {"A": "144 cm²", "B": "192 cm²", "C": "216 cm²", "D": "256 cm²"}, "correct_answer": "B"},
    {"id": 30, "difficulty": "medium", "question": "The ratio of areas of two similar triangles is 9:49. If a median of smaller triangle is 6 cm, find corresponding median of larger triangle.", "options": {"A": "8 cm", "B": "10 cm", "C": "12 cm", "D": "14 cm"}, "correct_answer": "D"},
    {"id": 31, "difficulty": "medium", "question": "If ΔABC ~ ΔDEF with ratio 2:3 and area(ΔABC)=48 cm², find area(ΔDEF).", "options": {"A": "72 cm²", "B": "96 cm²", "C": "108 cm²", "D": "120 cm²"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "Two similar triangles have corresponding sides in ratio 5:7. If difference of their areas is 144 cm², find area of larger triangle.", "options": {"A": "196 cm²", "B": "294 cm²", "C": "392 cm²", "D": "490 cm²"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "The areas of two similar triangles are 100 cm² and 400 cm². If a side of smaller triangle is 5 cm, find corresponding side of larger triangle.", "options": {"A": "10 cm", "B": "15 cm", "C": "20 cm", "D": "25 cm"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "ΔPQR ~ ΔXYZ. Area(PQR):Area(XYZ)=4:9. If PQ=8 cm, find XY.", "options": {"A": "10 cm", "B": "12 cm", "C": "14 cm", "D": "16 cm"}, "correct_answer": "B"},
    {"id": 35, "difficulty": "medium", "question": "Two similar triangles have corresponding altitudes 6 cm and 9 cm. If area of first triangle is 24 cm², find area of second.", "options": {"A": "36 cm²", "B": "48 cm²", "C": "54 cm²", "D": "64 cm²"}, "correct_answer": "C"},
    {"id": 36, "difficulty": "medium", "question": "The ratio of perimeters of two similar triangles is 4:7. What is ratio of their areas?", "options": {"A": "4:7", "B": "8:14", "C": "16:49", "D": "64:343"}, "correct_answer": "C"},
    {"id": 37, "difficulty": "medium", "question": "ΔABC ~ ΔDEF. Area(ΔABC)=75 cm², BC=10 cm, EF=15 cm. Find area(ΔDEF).", "options": {"A": "112.5 cm²", "B": "150 cm²", "C": "168.75 cm²", "D": "225 cm²"}, "correct_answer": "C"},
    {"id": 38, "difficulty": "medium", "question": "Two similar triangles have areas 64 cm² and 100 cm². If a side of smaller triangle is 8 cm, find perimeter of larger triangle if perimeter of smaller is 24 cm.", "options": {"A": "30 cm", "B": "32 cm", "C": "36 cm", "D": "40 cm"}, "correct_answer": "A"},
    {"id": 39, "difficulty": "medium", "question": "If the ratio of corresponding medians of two similar triangles is 3:8, find ratio of their areas.", "options": {"A": "3:8", "B": "9:64", "C": "27:512", "D": "6:16"}, "correct_answer": "B"},
    {"id": 40, "difficulty": "medium", "question": "ΔLMN ~ ΔXYZ with similarity ratio 5:6. If area(LMN)=125 cm², find area(XYZ).", "options": {"A": "150 cm²", "B": "175 cm²", "C": "180 cm²", "D": "216 cm²"}, "correct_answer": "C"},
    {"id": 41, "difficulty": "medium", "question": "The areas of two similar triangles are in ratio 1:9. If a side of smaller triangle is 3 cm, find corresponding side of larger triangle.", "options": {"A": "6 cm", "B": "9 cm", "C": "12 cm", "D": "15 cm"}, "correct_answer": "B"},
    {"id": 42, "difficulty": "medium", "question": "Two similar triangles have perimeters 20 cm and 35 cm. If area of larger is 245 cm², find area of smaller.", "options": {"A": "80 cm²", "B": "100 cm²", "C": "120 cm²", "D": "140 cm²"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "If ratio of areas is 25:36 and a side of first triangle is 15 cm, find corresponding side of second triangle.", "options": {"A": "16 cm", "B": "17 cm", "C": "18 cm", "D": "20 cm"}, "correct_answer": "C"},
    {"id": 44, "difficulty": "medium", "question": "ΔABC ~ ΔPQR. AB=12 cm, PQ=18 cm. If altitude from C to AB=8 cm, find altitude from R to PQ.", "options": {"A": "10 cm", "B": "12 cm", "C": "14 cm", "D": "16 cm"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "medium", "question": "Two similar triangles have areas 49 cm² and 81 cm². If a median of larger triangle is 13.5 cm, find corresponding median of smaller.", "options": {"A": "9 cm", "B": "10.5 cm", "C": "12 cm", "D": "14 cm"}, "correct_answer": "B"},
    {"id": 46, "difficulty": "medium", "question": "The ratio of corresponding sides of two similar triangles is 2:5. If area of smaller is 28 cm², find area of larger.", "options": {"A": "70 cm²", "B": "140 cm²", "C": "175 cm²", "D": "350 cm²"}, "correct_answer": "C"},
    {"id": 47, "difficulty": "medium", "question": "ΔDEF ~ ΔMNO. Area(DEF)=96 cm², area(MNO)=216 cm². If DE=12 cm, find MN.", "options": {"A": "15 cm", "B": "16 cm", "C": "18 cm", "D": "20 cm"}, "correct_answer": "C"},
    {"id": 48, "difficulty": "medium", "question": "Two similar triangles have corresponding altitudes 8 cm and 12 cm. If area of larger is 108 cm², find area of smaller.", "options": {"A": "48 cm²", "B": "54 cm²", "C": "64 cm²", "D": "72 cm²"}, "correct_answer": "A"},
    {"id": 49, "difficulty": "medium", "question": "If ratio of perimeters is 3:4 and area of smaller is 54 cm², find area of larger.", "options": {"A": "72 cm²", "B": "84 cm²", "C": "96 cm²", "D": "108 cm²"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "ΔABC ~ ΔXYZ. AB:XY=3:7. If area(ABC)=63 cm², find area(XYZ).", "options": {"A": "147 cm²", "B": "294 cm²", "C": "343 cm²", "D": "441 cm²"}, "correct_answer": "C"},
    {"id": 51, "difficulty": "medium", "question": "The areas of two similar triangles are 144 cm² and 225 cm². If perimeter of larger is 45 cm, find perimeter of smaller.", "options": {"A": "30 cm", "B": "32 cm", "C": "34 cm", "D": "36 cm"}, "correct_answer": "D"},
    {"id": 52, "difficulty": "medium", "question": "Two similar triangles have corresponding sides in ratio 4:9. If difference in their areas is 195 cm², find area of smaller triangle.", "options": {"A": "48 cm²", "B": "60 cm²", "C": "72 cm²", "D": "84 cm²"}, "correct_answer": "A"},
    {"id": 53, "difficulty": "medium", "question": "If ratio of areas is 16:81 and a side of first triangle is 8 cm, find corresponding side of second triangle.", "options": {"A": "12 cm", "B": "15 cm", "C": "18 cm", "D": "20 cm"}, "correct_answer": "C"},
    {"id": 54, "difficulty": "medium", "question": "ΔPQR ~ ΔLMN. PQ=15 cm, LM=25 cm. If altitude from Q to PR=12 cm, find altitude from M to LN.", "options": {"A": "16 cm", "B": "18 cm", "C": "20 cm", "D": "22 cm"}, "correct_answer": "C"},
    {"id": 55, "difficulty": "medium", "question": "Two similar triangles have perimeters 28 cm and 42 cm. If area of smaller is 98 cm², find area of larger.", "options": {"A": "196 cm²", "B": "220.5 cm²", "C": "245 cm²", "D": "294 cm²"}, "correct_answer": "B"},
    {"id": 56, "difficulty": "medium", "question": "The ratio of corresponding medians is 5:6. Find ratio of their areas.", "options": {"A": "5:6", "B": "10:12", "C": "25:36", "D": "125:216"}, "correct_answer": "C"},
    {"id": 57, "difficulty": "medium", "question": "ΔABC ~ ΔDEF with similarity ratio 4:5. If area(ABC)=128 cm², find area(DEF).", "options": {"A": "160 cm²", "B": "180 cm²", "C": "200 cm²", "D": "225 cm²"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "medium", "question": "Two similar triangles have areas 169 cm² and 289 cm². If a side of smaller is 13 cm, find corresponding side of larger.", "options": {"A": "15 cm", "B": "17 cm", "C": "19 cm", "D": "21 cm"}, "correct_answer": "B"},
    {"id": 59, "difficulty": "medium", "question": "If ratio of areas is 49:64 and perimeter of smaller is 35 cm, find perimeter of larger.", "options": {"A": "40 cm", "B": "42 cm", "C": "44 cm", "D": "48 cm"}, "correct_answer": "A"},
    {"id": 60, "difficulty": "medium", "question": "ΔXYZ ~ ΔUVW. XY:UV=3:8. If area(XYZ)=54 cm², find area(UVW).", "options": {"A": "144 cm²", "B": "288 cm²", "C": "384 cm²", "D": "432 cm²"}, "correct_answer": "C"},
    {"id": 61, "difficulty": "medium", "question": "The areas of two similar triangles are 81 cm² and 121 cm². If altitude of smaller triangle is 9 cm, find corresponding altitude of larger.", "options": {"A": "10 cm", "B": "11 cm", "C": "12 cm", "D": "13 cm"}, "correct_answer": "B"},
    {"id": 62, "difficulty": "medium", "question": "Two similar triangles have corresponding sides in ratio 2:7. If sum of their areas is 265 cm², find area of larger triangle.", "options": {"A": "49 cm²", "B": "216 cm²", "C": "245 cm²", "D": "256 cm²"}, "correct_answer": "C"},
    {"id": 63, "difficulty": "medium", "question": "If ratio of areas is 9:25 and a median of first triangle is 12 cm, find corresponding median of second.", "options": {"A": "15 cm", "B": "18 cm", "C": "20 cm", "D": "25 cm"}, "correct_answer": "C"},
    {"id": 64, "difficulty": "medium", "question": "ΔABC ~ ΔPQR. AB=18 cm, PQ=27 cm. If area(ABC)=162 cm², find area(PQR).", "options": {"A": "243 cm²", "B": "324 cm²", "C": "364.5 cm²", "D": "405 cm²"}, "correct_answer": "C"},
    {"id": 65, "difficulty": "medium", "question": "Two similar triangles have perimeters 24 cm and 36 cm. If area of larger is 180 cm², find area of smaller.", "options": {"A": "80 cm²", "B": "90 cm²", "C": "100 cm²", "D": "120 cm²"}, "correct_answer": "A"},
    {"id": 66, "difficulty": "medium", "question": "The ratio of corresponding altitudes is 3:5. If area of smaller is 54 cm², find area of larger.", "options": {"A": "90 cm²", "B": "120 cm²", "C": "150 cm²", "D": "180 cm²"}, "correct_answer": "C"},
    {"id": 67, "difficulty": "medium", "question": "If similarity ratio is 4:9 and area of smaller is 48 cm², find area of larger.", "options": {"A": "108 cm²", "B": "162 cm²", "C": "192 cm²", "D": "243 cm²"}, "correct_answer": "D"},
    {"id": 68, "difficulty": "medium", "question": "Two similar triangles have areas 196 cm² and 324 cm². If a side of larger is 18 cm, find corresponding side of smaller.", "options": {"A": "12 cm", "B": "14 cm", "C": "16 cm", "D": "17 cm"}, "correct_answer": "B"},
    {"id": 69, "difficulty": "medium", "question": "ΔLMN ~ ΔXYZ. Area(LMN):Area(XYZ)=9:16. If LM=12 cm, find XY.", "options": {"A": "14 cm", "B": "15 cm", "C": "16 cm", "D": "18 cm"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "If ratio of perimeters is 5:8 and area of smaller is 125 cm², find area of larger.", "options": {"A": "200 cm²", "B": "256 cm²", "C": "320 cm²", "D": "400 cm²"}, "correct_answer": "C"},
    {"id": 71, "difficulty": "medium", "question": "The areas of two similar triangles are 100 cm² and 225 cm². If perimeter of smaller is 30 cm, find perimeter of larger.", "options": {"A": "40 cm", "B": "45 cm", "C": "50 cm", "D": "55 cm"}, "correct_answer": "B"},
    {"id": 72, "difficulty": "medium", "question": "Two similar triangles have corresponding sides in ratio 3:10. If area of smaller is 27 cm², find area of larger.", "options": {"A": "90 cm²", "B": "270 cm²", "C": "300 cm²", "D": "900 cm²"}, "correct_answer": "C"},
    {"id": 73, "difficulty": "medium", "question": "If ratio of areas is 36:49 and a side of first triangle is 24 cm, find corresponding side of second.", "options": {"A": "26 cm", "B": "27 cm", "C": "28 cm", "D": "30 cm"}, "correct_answer": "C"},
    {"id": 74, "difficulty": "medium", "question": "ΔABC ~ ΔDEF. AB=16 cm, DE=20 cm. If altitude from C to AB=10 cm, find altitude from F to DE.", "options": {"A": "11.5 cm", "B": "12 cm", "C": "12.5 cm", "D": "13 cm"}, "correct_answer": "C"},
    {"id": 75, "difficulty": "medium", "question": "Two similar triangles have perimeters 32 cm and 56 cm. If area of smaller is 128 cm², find area of larger.", "options": {"A": "224 cm²", "B": "336 cm²", "C": "392 cm²", "D": "448 cm²"}, "correct_answer": "C"},
    {"id": 76, "difficulty": "medium", "question": "The ratio of corresponding medians is 7:9. Find ratio of their areas.", "options": {"A": "7:9", "B": "14:18", "C": "49:81", "D": "343:729"}, "correct_answer": "C"},
    {"id": 77, "difficulty": "medium", "question": "If similarity ratio is 5:12 and area of smaller is 75 cm², find area of larger.", "options": {"A": "180 cm²", "B": "300 cm²", "C": "432 cm²", "D": "540 cm²"}, "correct_answer": "C"},
    {"id": 78, "difficulty": "medium", "question": "Two similar triangles have areas 256 cm² and 400 cm². If a side of smaller is 16 cm, find corresponding side of larger.", "options": {"A": "18 cm", "B": "20 cm", "C": "22 cm", "D": "25 cm"}, "correct_answer": "B"},
    {"id": 79, "difficulty": "medium", "question": "ΔPQR ~ ΔSTU. Area(PQR)=180 cm², area(STU)=320 cm². If PQ=15 cm, find ST.", "options": {"A": "18 cm", "B": "20 cm", "C": "22 cm", "D": "24 cm"}, "correct_answer": "B"},
    {"id": 80, "difficulty": "medium", "question": "If ratio of perimeters is 2:5 and area of larger is 500 cm², find area of smaller.", "options": {"A": "80 cm²", "B": "100 cm²", "C": "120 cm²", "D": "160 cm²"}, "correct_answer": "A"},
    
    {"id": 81, "difficulty": "hard", "question": "Two similar triangles have areas in ratio 4:25. The sum of their perimeters is 58 cm. Find perimeter of larger triangle.", "options": {"A": "30 cm", "B": "35 cm", "C": "40 cm", "D": "50 cm"}, "correct_answer": "D"},
    {"id": 82, "difficulty": "hard", "question": "ΔABC ~ ΔDEF. Area(ΔABC)=144 cm², area(ΔDEF)=400 cm². If BC=12 cm and EF=20 cm, verify if triangles are similar and find AB if DE=25 cm.", "options": {"A": "15 cm", "B": "18 cm", "C": "20 cm", "D": "24 cm"}, "correct_answer": "B"},
    {"id": 83, "difficulty": "hard", "question": "The ratio of areas of two similar triangles is 9:49. If a side of first triangle is 15 cm and corresponding side of second triangle is 35 cm, find ratio of their perimeters.", "options": {"A": "3:7", "B": "9:49", "C": "15:35", "D": "27:343"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "Two similar triangles have perimeters 45 cm and 75 cm. If area of larger triangle is 300 cm², find difference between their areas.", "options": {"A": "108 cm²", "B": "120 cm²", "C": "132 cm²", "D": "144 cm²"}, "correct_answer": "C"},
    {"id": 85, "difficulty": "hard", "question": "ΔPQR ~ ΔXYZ. PQ=8 cm, QR=12 cm, PR=10 cm. If area(ΔPQR)=96 cm² and XY=12 cm, find area(ΔXYZ) and perimeter of ΔXYZ.", "options": {"A": "216 cm², 45 cm", "B": "192 cm², 40 cm", "C": "216 cm², 42 cm", "D": "192 cm², 45 cm"}, "correct_answer": "A"},
    {"id": 86, "difficulty": "hard", "question": "The areas of two similar triangles are 64 cm² and 225 cm². If a median of smaller triangle is 8 cm, find corresponding median of larger triangle and ratio of their altitudes.", "options": {"A": "15 cm, 8:15", "B": "12 cm, 8:12", "C": "18 cm, 8:18", "D": "20 cm, 8:20"}, "correct_answer": "A"},
    {"id": 87, "difficulty": "hard", "question": "Two similar triangles have corresponding sides in ratio 3:8. If sum of their areas is 365 cm², find both areas.", "options": {"A": "45 cm², 320 cm²", "B": "36 cm², 329 cm²", "C": "27 cm², 338 cm²", "D": "18 cm², 347 cm²"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "ΔABC ~ ΔLMN with similarity ratio 5:7. If area(ΔABC)+area(ΔLMN)=296 cm², find both areas.", "options": {"A": "100 cm², 196 cm²", "B": "120 cm², 176 cm²", "C": "125 cm², 171 cm²", "D": "150 cm², 146 cm²"}, "correct_answer": "A"},
    {"id": 89, "difficulty": "hard", "question": "The ratio of perimeters of two similar triangles is 4:9. If difference of their areas is 260 cm², find area of smaller triangle.", "options": {"A": "64 cm²", "B": "80 cm²", "C": "96 cm²", "D": "112 cm²"}, "correct_answer": "B"},
    {"id": 90, "difficulty": "hard", "question": "Two similar triangles have areas 81 cm² and 256 cm². If a side of first triangle is 9 cm and corresponding side of second is 16 cm, find ratio of their corresponding medians.", "options": {"A": "9:16", "B": "81:256", "C": "3:4", "D": "√81:√256"}, "correct_answer": "A"},
    {"id": 91, "difficulty": "hard", "question": "ΔXYZ ~ ΔUVW. Area(ΔXYZ)=121 cm², area(ΔUVW)=289 cm². If perimeter of ΔXYZ=44 cm, find perimeter of ΔUVW and XY if UV=34 cm.", "options": {"A": "68 cm, 22 cm", "B": "66 cm, 20 cm", "C": "64 cm, 18 cm", "D": "62 cm, 16 cm"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "The ratio of corresponding altitudes of two similar triangles is 5:8. If difference of their areas is 234 cm², find both areas.", "options": {"A": "250 cm², 484 cm²", "B": "200 cm², 434 cm²", "C": "150 cm², 384 cm²", "D": "100 cm², 334 cm²"}, "correct_answer": "C"},
    {"id": 93, "difficulty": "hard", "question": "Two similar triangles have sides in ratio 2:5. If area of larger triangle is 250 cm² more than smaller, find area of smaller triangle.", "options": {"A": "40 cm²", "B": "50 cm²", "C": "60 cm²", "D": "70 cm²"}, "correct_answer": "A"},
    {"id": 94, "difficulty": "hard", "question": "ΔABC ~ ΔPQR. AB=6 cm, BC=8 cm, CA=10 cm. If area(ΔABC)=24 cm² and PQ=9 cm, find area(ΔPQR) and perimeter of ΔPQR.", "options": {"A": "54 cm², 36 cm", "B": "48 cm², 32 cm", "C": "54 cm², 34 cm", "D": "48 cm², 36 cm"}, "correct_answer": "A"},
    {"id": 95, "difficulty": "hard", "question": "The areas of two similar triangles are in ratio 16:81. If sum of a pair of corresponding sides is 38 cm, find both sides.", "options": {"A": "8 cm, 30 cm", "B": "10 cm, 28 cm", "C": "12 cm, 26 cm", "D": "14 cm, 24 cm"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "Two similar triangles have perimeters 36 cm and 54 cm. If difference of their areas is 180 cm², find area of larger triangle.", "options": {"A": "288 cm²", "B": "324 cm²", "C": "360 cm²", "D": "396 cm²"}, "correct_answer": "B"},
    {"id": 97, "difficulty": "hard", "question": "ΔDEF ~ ΔMNO. Area(ΔDEF)=100 cm², area(ΔMNO)=225 cm². If DE=10 cm and MN=15 cm, find ratio of their corresponding altitudes and medians.", "options": {"A": "2:3, 2:3", "B": "10:15, 10:15", "C": "100:225, 100:225", "D": "√100:√225, √100:√225"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "The ratio of areas of two similar triangles is 25:144. If a median of smaller triangle is 10 cm, find corresponding median of larger triangle and ratio of their perimeters.", "options": {"A": "24 cm, 5:12", "B": "20 cm, 5:12", "C": "24 cm, 25:144", "D": "20 cm, 25:144"}, "correct_answer": "A"},
    {"id": 99, "difficulty": "hard", "question": "Two similar triangles have corresponding sides in ratio 3:7. If sum of their areas is 1160 cm², find area of each triangle.", "options": {"A": "360 cm², 800 cm²", "B": "90 cm², 1070 cm²", "C": "180 cm², 980 cm²", "D": "270 cm², 890 cm²"}, "correct_answer": "B"},
    {"id": 100, "difficulty": "hard", "question": "ΔABC ~ ΔXYZ with AB:XY=4:9. If area(ΔABC) is 112 cm² less than area(ΔXYZ), find both areas.", "options": {"A": "64 cm², 176 cm²", "B": "72 cm², 184 cm²", "C": "80 cm², 192 cm²", "D": "88 cm², 200 cm²"}, "correct_answer": "A"}
  ]
}