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    Question

    In triangle GHI, a point J lies on side HI such that

    ∠GJH = ∠GJI. If GH = 50 cm, GI = 30 cm, and HI = 40 cm, find the length of HJ.
    A 20 cm Correct Answer Incorrect Answer
    B 16 cm Correct Answer Incorrect Answer
    C 40 cm Correct Answer Incorrect Answer
    D 25 cm Correct Answer Incorrect Answer

    Solution

    ATQ,

    Since ∠GJH = ∠GJI, GJ is the angle bisector of ∠G.

    Using the Angle Bisector Theorem:

    GH / GI = HJ / JI

    Let HJ = x cm

    Then JI = 40 - x cm

    So, 50 / 30 = x / (40 - x)

    ⇒ 5 / 3 = x / (40 - x)

    Cross-multiplying:

    5(40 - x) = 3x

    200 - 5x = 3x

    200 = 8x

    x = 25

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