Question

In $\Delta ABC$, AD is median of $\Delta ABC$ and BE is median of $\Delta ABD$.

If ar$\left(\Delta ABE\right)=$ 15 $c{m}^2$, then ar$\left(\Delta ABC\right)$ is

• A. 60 $c{m}^2$
• B. 50 $c{m}^2$
• C. 40 $c{m}^2$
• D. 30 $c{m}^2$

Answer 1

The correct option is A 60 $c{m}^2$

The median of any triangle divides the triangle into two triangles of equal area.

$BE$ is the median of triangle $△ABD$

$\therefore ar\left(△ABD\right)=2ar\left(△ABE\right)$

$\Rightarrow ar\left(△ABD\right)=2\times 15=30{cm}^2$

Now, $AD$ is the median of triangle $ABC$

$\therefore ar\left(△ABC\right)=2ar\left(△ABD\right)\Rightarrow ar\left(△ABC\right)=2\times 30=60{cm}^2$.