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Question
ΔABC~ΔPQR and ar(ΔABC) = 4, ar(ΔPQR) . If BC = 12cm, find QR.
Solution
Given : 𝑎𝑟 ( Δ 𝐴𝐵𝐶 ) = 4𝑎𝑟 (Δ 𝑃𝑄𝑅 )
`(ar (Δ AABC))/(ar(ΔPQR))=4/1`
∵ ΔABC ~ ΔPQR
∴` (ar(ΔABC))/(ar(ΔPQR))=(BC^2)/(QR^2)`
∴ `(BC^2)/(QR^2)=4/1`
⇒` QR^2=12^2/4`
⇒ `QR^2=36`
⇒ QR=6 cm
Hence, QR = 6 cm
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