Question

    In △ ABC, ∠ A = 90°. M is the midpoint of BC

    and D is a point on BC such that AD Ʇ BC. If AB = 7 cm and AC = 24 cm. then AD: AM is equal to:
    A 168 : 275 Correct Answer Incorrect Answer
    B 336 : 625 Correct Answer Incorrect Answer
    C 24 : 25 Correct Answer Incorrect Answer
    D 32 : 43 Correct Answer Incorrect Answer

    Solution

    In right angled ∆ABC, 90° at A BC = AB + AC = 7 + 24 = 49 + 576 = 625 ⇒ BC = √625 = 25 If, M is the midpoint of BC, then AM = MC = BM = 25/2 As we know, AD × BC = AB × AC ⇒ AD × 25 = 7 × 24 ⇒ AD = (7 × 24)/25 ∴ Ratio of AD : AM = (7 × 24)/25 : 25/2 = 336 : 625

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