Question

If Δ ABC , MN || BC .

If AN : AC= 5 : 8, find ar(Δ AMN) : ar(Δ ABC) 

Answer 1

Given : `"AN"/"AC" = 5/8`

To Find : `("Ar" triangle "AMN")/("Ar" triangle "ABC")`

In Δ AMN and Δ ABC

∠AMN = ∠ ACB     ....(corresponding angles)

∠ ABC = ∠ ACB

∴ Δ AMN ∼ Δ ABC   .....(AA corollary)

∴ `("Ar" triangle "AMN")/("Ar" triangle "ABC") = "AN"^2/"AC"^2`

[The ration of areas of two similar triangle is equal to the ratio of square of their corresponding sides.]

`= (5/8)^2`

`("Ar" triangle "AMN")/("Ar" triangle "ABC") = 25/64`

Required ratio is 25 : 64.