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Question
ΔABC~ΔDEF such that ar(ΔABC) = 64 cm2 and ar(ΔDEF) = `169cm^2`. If BC = 4cm, find EF.
Solution
We have Δ ABC ~ Δ DEF
If two triangles are similar then the ratio of their areas is equal to the ratio of the squares of their corresponding sides.
∴ `(area(ΔABC))/(area(ΔDEF))=((BC)/(EF))^2`
⇒ `64/169=((BC)/(EF))^2`
⇒` (8/13)^2=(4/(EF))^2`
⇒ `8/13=4/(EF)`
⇒ EF = 6.5 cm
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