Question

In $△ABC,AD,BE$ and $CF$ are medians, and $G$ is centroid. If $AD=15cm$, find $AG$.

• A. $5cm$
• B. $8cm$
• C. $10cm$
• D. $12cm$

Answer 1

The correct option is C $10cm$

We know that centroid divides a median in the ratio $2:1$.

So, $G$ divides $AD$ in the ratio $2:1$.

Let $GD=x$, then $AG=2x$.

$\because AD=AG+GD$

$\therefore 15=2x+x$

$\Rightarrow 3x=15$

$\Rightarrow x=\frac{15}{3}=5cm$

$\Rightarrow AG=2x=2\times 5=10cm$