Question

Figure shows Δ KLM , P an T on KL and KM respectively such that∠ KLM =∠ KTP. 

If `"KL"/"KT" = 9/5` , find `("Ar" triangle "KLM")/("Ar" triangle "KTP")`.

Answer 1

Given : `"KL"/"KT"= 9/5`

To find : `("Ar" triangle "KLM")/("Ar" triangle "KTP")`

Sol : In Δ KLM and Δ KTP

∠ KLM =∠ KTP   ....(Given)

∠ LKM = ∠ TKP  ....(common)

Δ KLM and Δ KTP   ......(AA corollary)

`therefore ("Ar" triangle "KLM")/("Ar" triangle "KTP") = ("KL"/"KT")^2 = (9/5)^2 = 81/25`

i.e., 81 : 25

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