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.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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