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    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?
    A 12 cm Correct Answer Incorrect Answer
    B 18 cm Correct Answer Incorrect Answer
    C 24 cm Correct Answer Incorrect Answer
    D 10 cm Correct Answer Incorrect Answer

    Solution

    ATQ, Sides: 13, 14, 15. Semiperimeter s = (13 + 14 + 15)/2 = 42/2 = 21. Area by HeronтАЩs formula: Area = тИЪ[s(s тИТ a)(s тИТ b)(s тИТ c)] = тИЪ[21┬╖(21 тИТ 13)┬╖(21 тИТ 14)┬╖(21 тИТ 15)] = тИЪ[21┬╖8┬╖7┬╖6] = тИЪ7056 = 84 cm┬▓. Let h be the altitude from A to BC (which is 14 cm). Area = ┬╜ ├Ч BC ├Ч h тЗТ 84 = ┬╜ ├Ч 14 ├Ч h 84 = 7h тЗТ h = 12 cm.

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