Question

[4]
A ABC and A DEF are equilateral triangle. If
A ( ABC); A (A DEF) = 1:2 and AB = 4, find DE.​

Answer 1

$Consider,A (ΔABC): A(ΔDEF) = 1:2$

$⇒ \frac{A(ΔABC)}{A(ΔDEF)} = \frac{1}{2}$

$⇒ \frac{{AB}^{2} }{ {DE}^{2} } = \frac{1}{2}$

${⇒DE}^{2} = {2AB}^{2}$

$⇒ {DE}^{2} = {2 \times 4}^{2} </p><p> \: [∴AB=4]</p><p></p><p>$

$⇒DE= \sqrt{32}$

$⇒DE=4 \sqrt{2}$