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P-2 Similarity — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsP-2 Similarity3 Marks
Question
Δ ABC and ΔDEF are equilateral triangles. If A(ΔABC) : A(ΔDEF) = 1 : 2 and AB = 4, find DE.
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Answer

We know that, all the angles of an equilateral triangles are equal, i.e., $60^{\circ}$.
$\begin{array}{l}
\Rightarrow \triangle ABC \sim \triangle DEF \\
\Rightarrow \frac{ A (\triangle ABC )}{ A (\triangle DEF )}=\frac{ AB ^2}{ DE ^2} \\
\text { And, } \frac{ A (\triangle ABC )}{ A (\triangle DEF )}=\frac{1}{2} \text { (Given) } \\
\Rightarrow \frac{ AB ^2}{ DE ^2}=\frac{1}{2} \\
\Rightarrow D E^2=2 \times 4^2(\because A B=4) \\
\Rightarrow D E=\sqrt{32} \\
\Rightarrow D E=4 \sqrt{2} \\
\end{array}$
(By AAA Similarity Test)

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