Question

$ABC$ and $BDE$ are two equilateral triangles such that $D$ is the mid point of $BC$. Ratio of the areas of triangle $ABC$ and $BDE$ is

• A. $2:1$
• B. $1:2$
• C. $4:1$
• D. $1:4$

Answer 1

The correct option is C $4:1$

$△ABC\sim △BDE$ (both are equilateral triangles)

According to the given condition, $BC=\frac{BD}{2}$

$\Rightarrow △ABC:△BDE=A{B}^2:B{D}^2$

$=A{B}^2:(\frac{1}{2}BC{)}^2$

$=A{B}^2:\frac{1}{4}B{C}^2$

$=4:1$ $(\because AB=BC)$