Choose the correct alternative: ΔABC and ΔDEF are equilateral triangles. If ar(ΔABC): ar(ΔDEF) = 1 : 2 and AB = 4, then what is the length of DE?

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KollegeApply · Accepted Answer

underline(4sqrt 2) Explanation: Given, ΔABC and ΔDEF are equilateral triangles. $\therefore$ ΔABC ∼ ΔDEF $\Rightarrow$ `(ar(ΔABC))/(ar(ΔDEF)) = (AB^2)/(DE^2)` ......(By the theorem of ratio of areas of similar triangles.) $\Rightarrow$ $\frac{1}{2}$ = 4^2/(DE^2) .......`[∵ (A(ΔABC))/(A(ΔDEF)) = $\frac{1}{2}$, AB = 4 ("Given")]` $\Rightarrow$ DE2 = 2 $\times$ 42 $\Rightarrow$ DE2 = 32 $\Rightarrow$ DE = sqrt(32) $\Rightarrow$ DE = sqrt(16 xx 2) DE = 4sqrt(2)

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