Question

The height of triangle ABC is 40 cm and its area is 100 $c{m}^2$. In triangle ADE, DE = $\frac{1}{2}$BC. If the areas of these triangles are equal then find height of triangle ADE (in cm).

• A. 80

Answer 1

The correct option is A 80
Area of triangle ABC = $\frac{1}{2}\times 40\times BC$,

Area of triangle ADE= $\frac{1}{2}\times y\times DE$, and these areas are equal. Also DE= $\frac{1}{2}$BC.

$\therefore \frac{40\times BC}{2}=\frac{y\times DE}{2}$
$⟹\frac{40\times BC}{2}=\frac{y\times BC}{2\times 2}$

This simplifies to y=80. Hence, height of triangle ADE will be $80cm$.