Question
In a triangle ABC, a point D lies on AB and points E and
F lie on BC such that DF is parallel to AC and DE is parallel to AF. If BE = 4 cm. EF = 6cm. then find the length (in cm) of BC.Solution
Δ BDE ~ Δ BAF -------- (i) Δ BDF ~ Δ ABC ------- (ii) From (i), => x/(x+y) = 4/10 ------- (iii) From (ii), => x/(x+y) = 10/(10+t) ------- (iv) Now using (iii) in (iv) we get, => 4/10 = 10/(10+t) => 20 + 2t = 50 => t = 15 Therefore, BC = 4 + 6 + 15 = 25 cm
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