Question

In $\Delta ABC$ medians $BE$ and $CF$ intersect at $G$. If the straight line $AGD$ meets $BC$ in $D$ in such a way that $GD=1.5cm$, then the length of $AD$ is:

• A. $2.5cm$
• B. $3cm$
• C. $4cm$
• D. $4.5cm$

Answer 1

The correct option is D $4.5cm$

$G$ is the centroid of $\Delta ABC$
$\Rightarrow AG:GD=2:1$
$\Rightarrow AG:1.5=2:1$
$\Rightarrow \frac{AG}{1.5}=\frac{2}{1}\Rightarrow AG=2\times 1.5=3$
$\therefore AD=AG+GD=3+1.5=4.5cm$.