Question

    In triangle PQR, a point S is on QR such that ∠PSQ =

    ∠SPR. If PQ = 60 cm, PR = 45 cm, and QR = 35 cm, find the length of QS.
    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 ∠PSQ = ∠SPR, PS is the angle bisector of ∠P.

    Using Angle Bisector Theorem:

    PQ / PR = QS / SR

    Let QS = x cm

    Then SR = 35 - x cm

    60 / 45 = x / (35 - x)

    ⇒ 4 / 3 = x / (35 - x)

    Cross-multiplying:

    4(35 - x) = 3x

    140 - 4x = 3x

    140 = 7x

    x = 20

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