Question

In $△ABC,$ the medians $BE$ and $CF$ intersect at $G.AGD$ is a line meeting $BC$ at $D.$ If $GD$ is $1.5cm,$ then $AD$ is equal to -

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

Answer 1

The correct option is D

4.5 cm

SInce, $AD$ is the median and $G$ is centroid, (AG : GD = 2 : 1\)

$\Rightarrow GD:AD=1:3$

$\Rightarrow AD:GD=3:1$

$\Rightarrow \frac{AD}{GD}=\frac{3}{1}$

$\Rightarrow \frac{AD}{1.5}=3$

$\Rightarrow AD=4.5cm$