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Question
It is given that ΔABC ~ ΔPQR, with `(BC)/(QR) = 1/3`, then `(ar(ΔPRQ))/(ar(ΔBCA))` = ______.
Fill in the Blanks
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Solution
It is given that ΔABC ~ ΔPQR, with `(BC)/(QR) = 1/3`, then `(ar(ΔPRQ))/(ar(ΔBCA))` = 9.
Explanation:
Since ΔABC ~ ΔPQR, corresponding sides are proportional:
`(AB)/(PQ) = (BC)/(QR) = (CA)/(RP)`
So `(ar(ΔPRQ))/(ar(ΔBCA)) = (QR)/(BC^2)`
= (3)2
= 9
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