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Question
In Δ ABC, DE || BC; DC and EB intersects at F. if `"DE"/"BC" = 2/7` , find `("Ar" (triangle "FDE"))/("Ar" (triangle "FBC"))`
Solution
Given : `"DE"/"BC" = 2/7`
To find : (similar sides of similar triangles)
In Δ FDE and Δ FCB
∠ FDE = ∠ FCB
∠ FED = ∠ FBC .........(Alternate interior angles)
Δ FDE ∼ Δ FCB ...........(AA corollary)
`("Ar" (triangle "FDE"))/("Ar" (triangle "FBC")) = "DE"^2/"BC"^2 = (2/7)^2 = 4/49`
[The ration of areas of two similar triangle is equal to the ratio of square of their corresponding sides.]
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