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Find the radius of the circle inscribed in a triangle whose sides are 8 cm, 15 cm and 17 cm.
- a)4 cm
- b)5 cm
- c)3 cm
- d)2√2 cm
Correct answer is option 'C'. Can you explain this answer?
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Step 1: Find the semi-perimeter of the triangle
- The semi-perimeter of a triangle is calculated by adding all three sides of the triangle and dividing by 2.
- In this case, the sides of the triangle are 8 cm, 15 cm, and 17 cm.
- The semi-perimeter, s, is given by s = (8 + 15 + 17) / 2 = 20 cm.
Step 2: Use Heron's Formula to find the area of the triangle
- Heron's formula states that the area of a triangle with sides a, b, and c and semi-perimeter s is given by the formula:
Area = √(s(s - a)(s - b)(s - c))
- Substituting the values, we get Area = √(20(20 - 8)(20 - 15)(20 - 17)) = √(20*12*5*3) = √(3600) = 60 cm².
Step 3: Use the formula for the radius of the inscribed circle
- The radius of the inscribed circle in a triangle with sides a, b, and c and area A is given by the formula:
Radius = A/s
- Substituting the values, we get Radius = 60/20 = 3 cm.
Therefore, the radius of the circle inscribed in the triangle with sides 8 cm, 15 cm, and 17 cm is 3 cm. Hence, the correct answer is option 'C'.
- The semi-perimeter of a triangle is calculated by adding all three sides of the triangle and dividing by 2.
- In this case, the sides of the triangle are 8 cm, 15 cm, and 17 cm.
- The semi-perimeter, s, is given by s = (8 + 15 + 17) / 2 = 20 cm.
Step 2: Use Heron's Formula to find the area of the triangle
- Heron's formula states that the area of a triangle with sides a, b, and c and semi-perimeter s is given by the formula:
Area = √(s(s - a)(s - b)(s - c))
- Substituting the values, we get Area = √(20(20 - 8)(20 - 15)(20 - 17)) = √(20*12*5*3) = √(3600) = 60 cm².
Step 3: Use the formula for the radius of the inscribed circle
- The radius of the inscribed circle in a triangle with sides a, b, and c and area A is given by the formula:
Radius = A/s
- Substituting the values, we get Radius = 60/20 = 3 cm.
Therefore, the radius of the circle inscribed in the triangle with sides 8 cm, 15 cm, and 17 cm is 3 cm. Hence, the correct answer is option 'C'.
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Find the radius of the circle inscribed in a triangle whose sides are 8 cm, 15 cm and 17 cm.a)4 cmb)5 cmc)3 cmd)2√2 cmCorrect answer is option 'C'. Can you explain this answer?
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Find the radius of the circle inscribed in a triangle whose sides are 8 cm, 15 cm and 17 cm.a)4 cmb)5 cmc)3 cmd)2√2 cmCorrect answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about Find the radius of the circle inscribed in a triangle whose sides are 8 cm, 15 cm and 17 cm.a)4 cmb)5 cmc)3 cmd)2√2 cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the radius of the circle inscribed in a triangle whose sides are 8 cm, 15 cm and 17 cm.a)4 cmb)5 cmc)3 cmd)2√2 cmCorrect answer is option 'C'. Can you explain this answer?.
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