Question

In the given figure, $AE\parallel BC$ and $D$ is the mid-point of $BC$. If area $\left(△ABC\right)=x\times area\left(△EDC\right)$, then find the value of $x$.

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

In the given figure, $BD=DC$ as $D$ is the midpoint of $BC$.

Also $△ABC$ and $△EDC$ have same height as both have base and vertex on parallel lines.

$\therefore$ Ratio of areas of both depends on their base i.e $BC$ and $DC$.

$\therefore x=2$ as $BC=2\times DC$