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    Question

    The sides of a triangle are 13 cm, 14 cm, and 15 cm.

    What is the radius of the circumcircle of this triangle? 
    A 6 cm Correct Answer Incorrect Answer
    B 7 cm Correct Answer Incorrect Answer
    C 8 cm Correct Answer Incorrect Answer
    D 9 cm Correct Answer Incorrect Answer

    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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