Question

In $\Delta ABC$, if $AD$ divides $BC$ in the ratio $m:n$, then area of $\Delta ABD:$ area of $\Delta ADC$ is _________.

• A. $n:m$
• B. $m:n$
• C. $(m+1):n$
• D. $m:(n+1)$

Answer 1

The correct option is B $m:n$

AD divides BC in the ratio $m:n$, then

$BD=mx$ and $DC=nx$

Area of $△ABD=\frac{1}{2}\times AD\times BD=\frac{1}{2}AD\times mx$

Similarly, area of $△ADC=\frac{1}{2}AD\times nx$

Thus, $\frac{ar\left(△ABD\right)}{ar\left(△ACD\right)}=\frac{m}{n}$