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.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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