Question

In given $\Delta$ABC, AD and BE are medians of triangle which intersect each other at point G. If area of $\Delta$BDG is $1$ $c{m}^2$, then what is the area of DCEG?

• A. $2c{m}^2$
• B. $3c{m}^2$
• C. $4c{m}^2$
• D. $1c{m}^2$

Answer 1

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

Let $at\left(AGE\right)=ac{m}^2$ and $at\left(GECD\right)=bc{m}^2$
$at\left(ABD\right)=at\left(ADC\right)$
$3=a+b$ ...........$\left(1\right)$
Also, $at\left(ABE\right)=at\left(BEC\right)$
$2+a=1+b$
$a=1,b=2$.