Question
In triangle ABC, the sides are AB = 13 cm, BC = 14 cm, and CA = 15 cm. What is the length of the altitude from vertex A to side BC?
Solution
ATQ, Sides: 13, 14, 15. Semiperimeter s = (13 + 14 + 15)/2 = 42/2 = 21. Area by 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. Let h be the altitude from A to BC (which is 14 cm). Area = ½ × BC × h ⇒ 84 = ½ × 14 × h 84 = 7h ⇒ h = 12 cm.
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