Select the appropriate alternative. ΔABC and ΔDEF are equilateral… - Vidyadip

MCQ

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

A
$2 \sqrt2$
B
4
C
8
✓
$4 \sqrt2$

✓

Answer

Correct option: D.

$4 \sqrt2$

Solution: We know that, all the angles of an equilateral triangles are equal, i.e., 60°.
⇒ Δ ABC~Δ DEF ……(By AAA Similarity Test)
$\Rightarrow \frac{ A (\triangle ABC )}{ A (\triangle DEF )}=\frac{ AB ^2}{ DE ^2} $
$ \text { And, } \frac{ A (\triangle ABC )}{ A (\Delta 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} $
$\Rightarrow D E=4 \sqrt2$
(A) doesn’t match the solution.
(B) doesn’t match the solution.
(C) doesn’t match the solution.

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