Question

IF ABC and BDE are two equlateral triangles such that D is the mid point of BC, then find ar $\left(△ABC\right):ar\left(△BDE\right).$

Answer 1

ABC and BDE are two equilateral triangles and D is the mid point of BC.

Let each side of $△ABC=a$
Then $BD=\frac{a}{2}$
$\therefore$ Each side of triangle side of triangle BDE will be $\frac{a}{2}$.
Now , $\frac{ar\left(△ABC\right)}{ar\left(△\right(BDE\left)\right)}=\frac{\frac{\sqrt{3}}{4}{a}^2}{\frac{\sqrt{3}}{4}{\left(\frac{a}{2}\right)}^2}=\frac{\frac{\sqrt{3}}{4}{a}^2}{\frac{1}{4}\times \frac{\sqrt{3}}{4}{a}^2}=\frac{4}{1}\therefore ar\left(△ABC\right):ar\left(△BDE\right)=4:1$