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. 4:3
• B. 4:5
• C. 2:3
• D. 1:1

Answer 1

The correct option is C 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.