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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")`.
Solution
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.]
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