Question

In  Δ ABC, DE || BC; DC and EB intersects at F. if `"DE"/"BC" = 2/7` , find `("Ar" (triangle "FDE"))/("Ar" (triangle "FBC"))`

Answer 1

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.]