Question
The sides of a triangle are 13 cm, 14 cm, and 15 cm.
What is the radius of the circumcircle of this triangle?Solution
The area of the triangle can be calculated using Heron's formula. The semiperimeter s = (13 + 14 + 15) / 2 = 21 cm. The area A = √[21(21 - 13)(21 - 14)(21 - 15)] = √[21 × 8 × 7 × 6] = √7056 = 84 cm². The circumradius R is given by R = (abc) / (4A), where a = 13, b = 14, c = 15. So R = (13 × 14 × 15) / (4 × 84) = 2730 / 336 = 8.125 cm ≈ 8 cm. Correct answer: c) 8 cm
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