If ΔABC ~ ΔDEF and ar(ΔABC) : ar(ΔDEF) = 25 : 4, then BC : EF is ______.

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KollegeApply · Accepted Answer

If ΔABC ~ ΔDEF and ar(ΔABC) : ar(ΔDEF) = 25 : 4, then BC : EF is 5 : 2. Explanation: Since △ABC ∼ △DEF, the ratio of their areas is equal to the square of the ratio of their corresponding sides: `"ar(ΔABC)"/"ar(ΔDEF)" = ((BC)/(EF))^2 Given, "ar(ΔABC)"/"ar(ΔDEF)" = $\frac{25}{4}$ So, ((BC)/(EF))^2 = $\frac{25}{4}$ (BC)/(EF) = sqrt($\frac{25}{4}$) (BC)/(EF) = $\frac{5}{2}$` $\therefore$ BC : EF = 5 : 2

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