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Question
If Δ ABC , MN || BC .
If AN : AC= 5 : 8, find ar(Δ AMN) : ar(Δ ABC)
Solution
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.
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