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    Question

    In triangle XYZ, a point M lies on YZ such that ∠XMY =

    ∠XMZ. Given XY = 54 cm, XZ = 36 cm, and YZ = 30 cm, find the length of YM.
    A 20 cm Correct Answer Incorrect Answer
    B 60 cm Correct Answer Incorrect Answer
    C 46 cm Correct Answer Incorrect Answer
    D 18 cm Correct Answer Incorrect Answer

    Solution

    ATQ,

    Since ∠XMY = ∠XMZ, XM is the angle bisector of ∠X.

    By Angle Bisector Theorem:

    XY / XZ = YM / MZ

    Let YM = x cm

    Then MZ = 30 - x cm

    54 / 36 = x / (30 - x)

    ⇒ 3 / 2 = x / (30 - x)

    Cross-multiplying:

    3(30 - x) = 2x

    90 - 3x = 2x

    90 = 5x

    x = 18

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