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Question
It is given that ΔABC ~ ΔPQR, with `(BC)/(QR) = 1/3`. Then, `(ar(PRQ))/(ar(BCA))` is equal to ______.
Options
9
3
`1/3`
`1/9`
Solution
It is given that ΔABC ~ ΔPQR, with `(BC)/(QR) = 1/3`. Then, `(ar(PRQ))/(ar(BCA))` is equal to 9.
Explanation:
Given, ∆ABC ~ ∆PQR and `("BC")/("QR") = 1/3`
We know that, the ratio of the areas of two similar triangles is equal to square of the ratio of their corresponding sides.
∴ `("ar(∆PRQ)")/("ar(∆BCA)") = ("QR")^2/("BC")^2 = (("QR")/("BC"))^2`
= `(3/1)^2`
= `9/1`
= 9
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