{
  "title": "Semi-perimeter (Heron's Formula) - Grade 9 CBSE",
  "total_questions": 100,
  "questions": [
    {"id": 1, "difficulty": "easy", "question": "What is the formula for semi-perimeter 's' of a triangle?", "options": {"A": "s = a + b + c", "B": "s = (a + b + c)/2", "C": "s = 2(a + b + c)", "D": "s = √(a + b + c)"}, "correct_answer": "B"},
    {"id": 2, "difficulty": "easy", "question": "If sides of triangle are 6cm, 8cm, 10cm, what is semi-perimeter?", "options": {"A": "10cm", "B": "11cm", "C": "12cm", "D": "13cm"}, "correct_answer": "C"},
    {"id": 3, "difficulty": "easy", "question": "Semi-perimeter is ______ of perimeter.", "options": {"A": "double", "B": "half", "C": "square", "D": "square root"}, "correct_answer": "D"},
    {"id": 4, "difficulty": "easy", "question": "For triangle with perimeter 24cm, semi-perimeter is:", "options": {"A": "10cm", "B": "11cm", "C": "12cm", "D": "13cm"}, "correct_answer": "A"},
    {"id": 5, "difficulty": "easy", "question": "What does 's' represent in Heron's formula?", "options": {"A": "Side", "B": "Sum", "C": "Semi-perimeter", "D": "Surface area"}, "correct_answer": "B"},
    {"id": 6, "difficulty": "easy", "question": "If sides are 5cm, 12cm, 13cm, calculate s.", "options": {"A": "13cm", "B": "14cm", "C": "15cm", "D": "16cm"}, "correct_answer": "C"},
    {"id": 7, "difficulty": "easy", "question": "For equilateral triangle of side 8cm, s equals:", "options": {"A": "10cm", "B": "11cm", "C": "12cm", "D": "13cm"}, "correct_answer": "C"},
    {"id": 8, "difficulty": "easy", "question": "Is semi-perimeter always greater than each side?", "options": {"A": "Yes", "B": "No", "C": "Sometimes", "D": "Cannot say"}, "correct_answer": "B"},
    {"id": 9, "difficulty": "easy", "question": "If a=7, b=8, c=9, then s = ?", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "C"},
    {"id": 10, "difficulty": "easy", "question": "Semi-perimeter is used in which formula?", "options": {"A": "Pythagoras", "B": "Heron's", "C": "Area of circle", "D": "Volume of sphere"}, "correct_answer": "A"},
    {"id": 11, "difficulty": "easy", "question": "For isosceles triangle with equal sides 5cm and base 6cm, s = ?", "options": {"A": "7cm", "B": "8cm", "C": "9cm", "D": "10cm"}, "correct_answer": "B"},
    {"id": 12, "difficulty": "easy", "question": "If perimeter = 30cm, then s = ?", "options": {"A": "13cm", "B": "14cm", "C": "15cm", "D": "16cm"}, "correct_answer": "D"},
    {"id": 13, "difficulty": "easy", "question": "What is relationship between s and perimeter P?", "options": {"A": "s = P/2", "B": "s = 2P", "C": "s = P²", "D": "s = √P"}, "correct_answer": "A"},
    {"id": 14, "difficulty": "easy", "question": "For sides 3, 4, 5, find semi-perimeter.", "options": {"A": "5", "B": "6", "C": "7", "D": "8"}, "correct_answer": "B"},
    {"id": 15, "difficulty": "easy", "question": "If triangle sides double, what happens to s?", "options": {"A": "Doubles", "B": "Halves", "C": "Quadruples", "D": "Same"}, "correct_answer": "A"},
    {"id": 16, "difficulty": "easy", "question": "Can s be less than longest side?", "options": {"A": "Always", "B": "Never", "C": "Sometimes", "D": "Cannot determine"}, "correct_answer": "C"},
    {"id": 17, "difficulty": "easy", "question": "For right triangle legs 6 and 8, s = ?", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "C"},
    {"id": 18, "difficulty": "easy", "question": "If s=15 and two sides are 7 and 10, third side is?", "options": {"A": "11", "B": "12", "C": "13", "D": "14"}, "correct_answer": "C"},
    {"id": 19, "difficulty": "easy", "question": "Semi-perimeter measured in what units?", "options": {"A": "Square units", "B": "Linear units", "C": "Cubic units", "D": "No units"}, "correct_answer": "B"},
    {"id": 20, "difficulty": "easy", "question": "For equilateral triangle, s = (3/2) × ?", "options": {"A": "Side", "B": "Perimeter", "C": "Area", "D": "Height"}, "correct_answer": "A"},
    {"id": 21, "difficulty": "medium", "question": "Triangle sides: 11cm, 60cm, 61cm. Find semi-perimeter.", "options": {"A": "64cm", "B": "65cm", "C": "66cm", "D": "67cm"}, "correct_answer": "C"},
    {"id": 22, "difficulty": "medium", "question": "If s=18 and a=6, b=8, find c.", "options": {"A": "20", "B": "21", "C": "22", "D": "23"}, "correct_answer": "C"},
    {"id": 23, "difficulty": "medium", "question": "For sides 7, 24, 25, calculate (s-a) where a=7.", "options": {"A": "21", "B": "22", "C": "23", "D": "24"}, "correct_answer": "D"},
    {"id": 24, "difficulty": "medium", "question": "Isosceles triangle: equal sides=13cm, base=10cm. Find s.", "options": {"A": "16cm", "B": "17cm", "C": "18cm", "D": "19cm"}, "correct_answer": "C"},
    {"id": 25, "difficulty": "medium", "question": "If perimeter=48cm and sides consecutive integers, find s.", "options": {"A": "22cm", "B": "23cm", "C": "24cm", "D": "25cm"}, "correct_answer": "C"},
    {"id": 26, "difficulty": "medium", "question": "For s=21 and sides ratio 2:3:4, find smallest side.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "C"},
    {"id": 27, "difficulty": "medium", "question": "Triangle: sides 9, 12, 15. Find (s-b) where b=12.", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "A"},
    {"id": 28, "difficulty": "medium", "question": "If s=28 and a=10, (s-b)=12, find b.", "options": {"A": "14", "B": "15", "C": "16", "D": "17"}, "correct_answer": "C"},
    {"id": 29, "difficulty": "medium", "question": "Right triangle: hypotenuse 29, one leg 20. Find s.", "options": {"A": "33", "B": "34", "C": "35", "D": "36"}, "correct_answer": "C"},
    {"id": 30, "difficulty": "medium", "question": "Sides: 8, 15, x. If s=25, find x.", "options": {"A": "22", "B": "23", "C": "24", "D": "25"}, "correct_answer": "A"},
    {"id": 31, "difficulty": "medium", "question": "For equilateral triangle, s=15cm. Find side length.", "options": {"A": "8cm", "B": "9cm", "C": "10cm", "D": "11cm"}, "correct_answer": "C"},
    {"id": 32, "difficulty": "medium", "question": "If s=30 and sides are 3 consecutive multiples of 4, find middle side.", "options": {"A": "10", "B": "12", "C": "14", "D": "16"}, "correct_answer": "B"},
    {"id": 33, "difficulty": "medium", "question": "Triangle: sides 16, 30, 34. Find (s-c) where c=34.", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "A"},
    {"id": 34, "difficulty": "medium", "question": "Isosceles: perimeter=40cm, base=12cm. Find s.", "options": {"A": "18cm", "B": "19cm", "C": "20cm", "D": "21cm"}, "correct_answer": "C"},
    {"id": 35, "difficulty": "medium", "question": "For sides 17, 25, 26, calculate s-a where a=17.", "options": {"A": "16", "B": "17", "C": "18", "D": "19"}, "correct_answer": "B"},
    {"id": 36, "difficulty": "medium", "question": "If s=27 and sides in arithmetic progression with common difference 3, find smallest side.", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "B"},
    {"id": 37, "difficulty": "medium", "question": "Right triangle legs 9 and 40. Find semi-perimeter.", "options": {"A": "44", "B": "45", "C": "46", "D": "47"}, "correct_answer": "B"},
    {"id": 38, "difficulty": "medium", "question": "Triangle: s=35, a=12, b=16. Find c.", "options": {"A": "40", "B": "41", "C": "42", "D": "43"}, "correct_answer": "C"},
    {"id": 39, "difficulty": "medium", "question": "For sides 14, 48, 50, find (s-b) where b=48.", "options": {"A": "8", "B": "9", "C": "10", "D": "11"}, "correct_answer": "A"},
    {"id": 40, "difficulty": "medium", "question": "If s=33 and a=10, b=15, find perimeter.", "options": {"A": "64", "B": "65", "C": "66", "D": "67"}, "correct_answer": "C"},
    {"id": 41, "difficulty": "medium", "question": "Isosceles: equal sides=25, perimeter=80. Find s.", "options": {"A": "38", "B": "39", "C": "40", "D": "41"}, "correct_answer": "C"},
    {"id": 42, "difficulty": "medium", "question": "Triangle sides: 18, 24, 30. Calculate s-c where c=30.", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "A"},
    {"id": 43, "difficulty": "medium", "question": "For s=42 and sides ratio 5:8:9, find largest side.", "options": {"A": "16", "B": "18", "C": "20", "D": "22"}, "correct_answer": "B"},
    {"id": 44, "difficulty": "medium", "question": "Right triangle: sides 20, 21, 29. Find (s-a) where a=20.", "options": {"A": "14", "B": "15", "C": "16", "D": "17"}, "correct_answer": "B"},
    {"id": 45, "difficulty": "medium", "question": "If perimeter=72 and s=36, verify triangle existence.", "options": {"A": "Always exists", "B": "Never exists", "C": "May exist", "D": "Invalid data"}, "correct_answer": "A"},
    {"id": 46, "difficulty": "medium", "question": "Triangle: sides 13, 20, 21. Find s-b where b=20.", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "B"},
    {"id": 47, "difficulty": "medium", "question": "For equilateral triangle, if s=18cm, find area.", "options": {"A": "36√3 cm²", "B": "54√3 cm²", "C": "72√3 cm²", "D": "108√3 cm²"}, "correct_answer": "D"},
    {"id": 48, "difficulty": "medium", "question": "Isosceles: base=14, area=84. Find s using Heron's formula concept.", "options": {"A": "24", "B": "25", "C": "26", "D": "27"}, "correct_answer": "C"},
    {"id": 49, "difficulty": "medium", "question": "If s=39 and two sides are 17 and 24, find third side.", "options": {"A": "35", "B": "36", "C": "37", "D": "38"}, "correct_answer": "C"},
    {"id": 50, "difficulty": "medium", "question": "Triangle sides: 10, 24, 26. Calculate (s-c) where c=26.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "D"},
    {"id": 51, "difficulty": "medium", "question": "For s=45 and sides consecutive multiples of 3, find perimeter.", "options": {"A": "86", "B": "88", "C": "90", "D": "92"}, "correct_answer": "C"},
    {"id": 52, "difficulty": "medium", "question": "Right triangle: hypotenuse 65, one leg 16. Find s.", "options": {"A": "70", "B": "71", "C": "72", "D": "73"}, "correct_answer": "D"},
    {"id": 53, "difficulty": "medium", "question": "If s=28.5 and sides are 9.5, 12, 15, verify.", "options": {"A": "Correct", "B": "Incorrect", "C": "Cannot verify", "D": "Partial correct"}, "correct_answer": "A"},
    {"id": 54, "difficulty": "medium", "question": "Triangle: sides 19, 20, 37. Find s-a where a=19.", "options": {"A": "18", "B": "19", "C": "20", "D": "21"}, "correct_answer": "B"},
    {"id": 55, "difficulty": "medium", "question": "For isosceles triangle, if s=32 and base=20, find equal side.", "options": {"A": "20", "B": "21", "C": "22", "D": "23"}, "correct_answer": "C"},
    {"id": 56, "difficulty": "medium", "question": "If s=25 and (s-a)=10, (s-b)=12, (s-c)=3, find sides.", "options": {"A": "15,13,22", "B": "14,12,23", "C": "15,13,23", "D": "14,13,22"}, "correct_answer": "A"},
    {"id": 57, "difficulty": "medium", "question": "Right triangle area=210, legs 20 and 21. Find s.", "options": {"A": "68", "B": "69", "C": "70", "D": "71"}, "correct_answer": "C"},
    {"id": 58, "difficulty": "medium", "question": "Triangle sides: 23, 27, 34. Calculate s-c where c=34.", "options": {"A": "10", "B": "11", "C": "12", "D": "13"}, "correct_answer": "D"},
    {"id": 59, "difficulty": "medium", "question": "For s=50 and sides ratio 3:5:7, find middle side.", "options": {"A": "18", "B": "20", "C": "22", "D": "24"}, "correct_answer": "B"},
    {"id": 60, "difficulty": "medium", "question": "Isosceles perimeter=52, base=18. Find s.", "options": {"A": "24", "B": "25", "C": "26", "D": "27"}, "correct_answer": "C"},
    {"id": 61, "difficulty": "medium", "question": "If s=44 and a=15, b=20, find c.", "options": {"A": "51", "B": "52", "C": "53", "D": "54"}, "correct_answer": "C"},
    {"id": 62, "difficulty": "medium", "question": "Triangle: sides 8.5, 7.5, 6.5. Find semi-perimeter.", "options": {"A": "10.5", "B": "11", "C": "11.25", "D": "11.5"}, "correct_answer": "C"},
    {"id": 63, "difficulty": "medium", "question": "For equilateral triangle, if s=21, find height.", "options": {"A": "7√3", "B": "8√3", "C": "9√3", "D": "10√3"}, "correct_answer": "A"},
    {"id": 64, "difficulty": "medium", "question": "Right triangle: sides 28, 45, 53. Find (s-b) where b=45.", "options": {"A": "17", "B": "18", "C": "19", "D": "20"}, "correct_answer": "B"},
    {"id": 65, "difficulty": "medium", "question": "If s=38 and sides differ by 4, find middle side.", "options": {"A": "12", "B": "13", "C": "14", "D": "15"}, "correct_answer": "C"},
    {"id": 66, "difficulty": "medium", "question": "Triangle: sides 15, 36, 39. Calculate s-a where a=15.", "options": {"A": "30", "B": "31", "C": "32", "D": "33"}, "correct_answer": "A"},
    {"id": 67, "difficulty": "medium", "question": "For isosceles, if s=30 and equal sides=17, find base.", "options": {"A": "24", "B": "25", "C": "26", "D": "27"}, "correct_answer": "C"},
    {"id": 68, "difficulty": "medium", "question": "If perimeter=84 and sides ratio 3:4:5, find s.", "options": {"A": "40", "B": "41", "C": "42", "D": "43"}, "correct_answer": "C"},
    {"id": 69, "difficulty": "medium", "question": "Right triangle: legs 11, 60. Find semi-perimeter.", "options": {"A": "64", "B": "65", "C": "66", "D": "67"}, "correct_answer": "C"},
    {"id": 70, "difficulty": "medium", "question": "Triangle: sides 12, 35, 37. Find (s-c) where c=37.", "options": {"A": "6", "B": "7", "C": "8", "D": "9"}, "correct_answer": "A"},
    {"id": 71, "difficulty": "medium", "question": "For s=29 and a=8, b=12, find perimeter.", "options": {"A": "56", "B": "57", "C": "58", "D": "59"}, "correct_answer": "C"},
    {"id": 72, "difficulty": "medium", "question": "Isosceles: area=120, base=16, equal sides=17. Verify s.", "options": {"A": "23", "B": "24", "C": "25", "D": "26"}, "correct_answer": "C"},
    {"id": 73, "difficulty": "medium", "question": "If s=47 and sides are prime numbers, find possible sides.", "options": {"A": "17,19,23", "B": "19,23,29", "C": "13,17,29", "D": "11,23,31"}, "correct_answer": "D"},
    {"id": 74, "difficulty": "medium", "question": "Triangle: sides 9, 40, 41. Calculate s-b where b=40.", "options": {"A": "4", "B": "5", "C": "6", "D": "7"}, "correct_answer": "B"},
    {"id": 75, "difficulty": "medium", "question": "For equilateral triangle, if s=27, find circumradius.", "options": {"A": "9√3", "B": "12√3", "C": "15√3", "D": "18√3"}, "correct_answer": "A"},
    {"id": 76, "difficulty": "medium", "question": "Right triangle: hypotenuse 85, one leg 13. Find s.", "options": {"A": "108", "B": "109", "C": "110", "D": "111"}, "correct_answer": "B"},
    {"id": 77, "difficulty": "medium", "question": "If s=33.5 and sides 10.5, 14, 19, verify.", "options": {"A": "Correct", "B": "Incorrect", "C": "Cannot determine", "D": "Approximately correct"}, "correct_answer": "A"},
    {"id": 78, "difficulty": "medium", "question": "Triangle: sides 21, 28, 35. Find s-a where a=21.", "options": {"A": "20", "B": "21", "C": "22", "D": "23"}, "correct_answer": "B"},
    {"id": 79, "difficulty": "medium", "question": "For isosceles, if s=34 and base=22, find equal side.", "options": {"A": "23", "B": "24", "C": "25", "D": "26"}, "correct_answer": "C"},
    {"id": 80, "difficulty": "medium", "question": "If s=41 and (s-a)=15, (s-b)=18, (s-c)=8, find perimeter.", "options": {"A": "80", "B": "81", "C": "82", "D": "83"}, "correct_answer": "C"},
    {"id": 81, "difficulty": "hard", "question": "Triangle sides: 13, 14, 15. Using s, calculate (s-a)(s-b)(s-c).", "options": {"A": "168", "B": "192", "C": "216", "D": "240"}, "correct_answer": "C"},
    {"id": 82, "difficulty": "hard", "question": "For triangle with s=28 and area=84√3, find if it's equilateral.", "options": {"A": "Yes, side=16", "B": "Yes, side=18", "C": "No", "D": "Insufficient data"}, "correct_answer": "B"},
    {"id": 83, "difficulty": "hard", "question": "If s=30 and area=30√14, find product (s-a)(s-b)(s-c).", "options": {"A": "1260", "B": "1280", "C": "1300", "D": "1320"}, "correct_answer": "A"},
    {"id": 84, "difficulty": "hard", "question": "Triangle sides satisfy s-a=4, s-b=6, s-c=8. Find area using Heron's.", "options": {"A": "12√15", "B": "24√15", "C": "36√15", "D": "48√15"}, "correct_answer": "B"},
    {"id": 85, "difficulty": "hard", "question": "For right triangle, s=30, hypotenuse=25. Find area.", "options": {"A": "120", "B": "150", "C": "180", "D": "210"}, "correct_answer": "B"},
    {"id": 86, "difficulty": "hard", "question": "If s=21 and area=21√15, find sides if they're consecutive integers.", "options": {"A": "6,7,8", "B": "7,8,9", "C": "8,9,10", "D": "9,10,11"}, "correct_answer": "B"},
    {"id": 87, "difficulty": "hard", "question": "Triangle has s=24 and (s-a):(s-b):(s-c)=1:2:3. Find area.", "options": {"A": "48√6", "B": "72√6", "C": "96√6", "D": "120√6"}, "correct_answer": "A"},
    {"id": 88, "difficulty": "hard", "question": "For isosceles triangle, s=32, area=120. Find base.", "options": {"A": "12", "B": "15", "C": "18", "D": "20"}, "correct_answer": "D"},
    {"id": 89, "difficulty": "hard", "question": "If s=35 and area=210, find possible sides for right triangle.", "options": {"A": "20,21,29", "B": "12,35,37", "C": "15,28,41", "D": "21,28,35"}, "correct_answer": "A"},
    {"id": 90, "difficulty": "hard", "question": "Triangle: s=40, area=60√39. Find sides if in arithmetic progression.", "options": {"A": "13,26,39", "B": "15,25,35", "C": "16,28,40", "D": "18,30,42"}, "correct_answer": "C"},
    {"id": 91, "difficulty": "hard", "question": "For equilateral triangle, if s=18√3, find area.", "options": {"A": "243√3", "B": "256√3", "C": "324√3", "D": "361√3"}, "correct_answer": "A"},
    {"id": 92, "difficulty": "hard", "question": "If s=42 and (s-a)(s-b)(s-c)=2016, find area.", "options": {"A": "84√6", "B": "96√6", "C": "108√6", "D": "120√6"}, "correct_answer": "A"},
    {"id": 93, "difficulty": "hard", "question": "Triangle sides: s=27, area=27√35. Verify sides 7, 24, 25.", "options": {"A": "Correct", "B": "Incorrect", "C": "Partial", "D": "Cannot verify"}, "correct_answer": "B"},
    {"id": 94, "difficulty": "hard", "question": "For right triangle, s=56, area=336. Find hypotenuse.", "options": {"A": "48", "B": "50", "C": "52", "D": "54"}, "correct_answer": "B"},
    {"id": 95, "difficulty": "hard", "question": "If s=45 and sides in geometric progression with ratio 2, find area.", "options": {"A": "270", "B": "315", "C": "360", "D": "405"}, "correct_answer": "A"},
    {"id": 96, "difficulty": "hard", "question": "Triangle: s=39, area=156√3. Find if it's 30-60-90 triangle.", "options": {"A": "Yes", "B": "No", "C": "Maybe", "D": "Insufficient"}, "correct_answer": "B"},
    {"id": 97, "difficulty": "hard", "question": "For isosceles, s=34, area=240. Find equal sides.", "options": {"A": "25", "B": "26", "C": "27", "D": "28"}, "correct_answer": "A"},
    {"id": 98, "difficulty": "hard", "question": "If s=50 and area=300√7, find sides ratio 3:5:7.", "options": {"A": "15,25,35", "B": "18,30,42", "C": "21,35,49", "D": "24,40,56"}, "correct_answer": "B"},
    {"id": 99, "difficulty": "hard", "question": "Triangle: s=33, (s-a)=11, (s-b)=12, (s-c)=10. Find exact area.", "options": {"A": "22√130", "B": "44√30", "C": "66√10", "D": "132√5"}, "correct_answer": "C"},
    {"id": 100, "difficulty": "hard", "question": "For equilateral triangle, if s=15√3, find inscribed circle radius.", "options": {"A": "5", "B": "5√3", "C": "10", "D": "10√3"}, "correct_answer": "A"}
  ]
}