Question
A triangle has sides 13 cm, 14 cm, and 15 cm. What is
the radius of its incircle?Solution
Sides: a = 13, b = 14, c = 15. Semi-perimeter s = (13 + 14 + 15) / 2 = 42/2 = 21. Area (Heron’s formula): Area = √[s(s − a)(s − b)(s − c)] = √[21 × (21 − 13) × (21 − 14) × (21 − 15)] = √[21 × 8 × 7 × 6] = √7056 = 84 cm². Inradius r = Area / s = 84 / 21 = 4 cm.
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