Question

D and E are the points on the sides AB and AC respectively of triangle ABC such that $DE||BC$. If area of $△DBC=15c{m}^2$, then area of $△EBC$ is:

• A. $30c{m}^2$
• B. $7.5c{m}^2$
• C. $15c{m}^2$
• D. $20c{m}^2$

Answer 1

Answer: (C)

$15c{m}^2$

Given, $DE||BC$

Therefore, the altitudes of $△EBC$ and $△DBC$ are equal.

Also, they have a common base $BC$.

Thus, $\text{Ar}\left(△EBC\right)=\text{Ar}\left(△DBC\right)$

$\Rightarrow \text{Ar}\left(△EBC\right)=15{\text{cm}}^2$