Question

Find the ratio in which D divides side BC if $\frac{Ar\left(\Delta ABD\right)}{Ar\left(\Delta ADC\right)}=\frac{2}{3}$.

• A. $\frac{4}{3}$
• B. $\sqrt{\frac{2}{3}}$
• C. $\frac{2}{3}$
• D. $1$

Answer 1

The correct option is C

$\frac{2}{3}$

In $\Delta ABD$ and $\Delta ADC$, the height is common as it is the perpendicular distance from point A to side BC.
$\frac{Ar\left(ABD\right)}{Ar\left(ADC\right)}=\frac{\left(\frac{1}{2}\right)\left(BaseBD\right)\left(HeightAE\right)}{\left(\frac{1}{2}\right)\left(BaseDC\right)\left(HeightAE\right)}=\frac{BD}{DC}=\frac{2}{3}$ i.e. D divides BC in the ratio 2:3.