Question

If AD is the median of a triangle ABC and area of triangle $ADC=15c{m}^2$, then $\frac{ar\left(\Delta ABC\right)}{15}=$ ____.

• A. $\frac{9}{3}c{m}^2$
• B. $4c{m}^2$
• C. $\frac{16}{4}c{m}^2$
• D. $2c{m}^2$

Answer 1

The correct option is D

$2c{m}^2$

Since AD is the median of $\Delta ABC$
$\therefore ar\left(\Delta ABD\right)=ar\left(\Delta ADC\right)$

$=\frac{1}{2}ar\left(\Delta ABC\right)=15$
($\because$ The median of a triangle divides it into two triangle of equal areas)
$\Rightarrow \frac{1}{2}ar\left(\Delta ABC\right)=15$
$\Rightarrow \frac{ar\left(\Delta ABC\right)}{15}=2$