Question

$ABC$ and $BDE$ are two equilateral triangles such that $D$ is the mid point of $BC$. If the ratio of the area of triangle $ABC$ and $BDE$ is $m:1$, find $m$

Answer 1

Area of BDE $=a^2\times \frac{\sqrt{3}}{4}$

Area of ABC $={\left(2a\right)}^2\times \frac{\sqrt{3}}{4}=\sqrt{3}\times a^2$

Ratio $=\frac{\sqrt{3}{a}^2}{\sqrt{3}{a}^2}\times 4$

$=4:1$