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Question
ΔPQR ~ ΔABC, `(PR)/(AC) = 5/7`, then
Options
ΔABC is greater.
ΔPQR is greater.
Both triangles are congruent.
Can’t say.
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Solution
ΔABC is greater.
Explanation:
Similar triangles have corresponding sides in the same ratio, so the scale factor from ΔABC to ΔPQR is:
`(PR)/(AC) = 5/7 (< 1)`
Meaning each side of ΔPQR is `5/7` of the corresponding side of ΔABC.
Areas scale as the square of the side ratio, so:
`(Area(PQR))/(Area(ABC)) = (5/7)^2 = 25/49 < 1`
Therefore, ΔABC is greater.
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