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Question
∆ABC ∼ ∆PQR such that ar(∆ABC) = 4 ar(∆PQR). If BC = 12 cm, then QR =
Options
9 cm
10 cm
6 cm
8 cm
Solution
Given: In Δ ABC and ΔPQR
`Δ ABC ∼ Δ PQR`
`Ar (Δ ABC) = 4Ar (Δ PQR)`
`BC=12 cm`
To find: Measure of QR
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
`(Ar(Δ ABC))/(Ar(Δ PQR))=(BC)^2/(QR)^2`
`(4Ar(Δ ABC))/(Ar(Δ PQR))=12^2/(QR^2)`(Give Ar(Δ ABC)=4Ar (Δ PQR))
`4/1=12^2/(QR^2)`
`2/1=12/(QR)`
Hence the correct answer is `c`
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