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.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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