Question

In $△ABC$, $AB=9$cm , $BC=10$cm and $AC=13$cm.If $G$ is centroid of $△ABC$ and $D$ is midpoint of $BC$ then the length of $GD$ is

• A. $25$
• B. $20$
• C. $\frac{10}{3}$
• D. $\frac{20}{3}$

Answer 1

The correct option is C $\frac{10}{3}$

AD is median of ABC

$A{D}^2=\frac{1}{4}[2A{B}^2+2A{C}^2-B{C}^2]$

$=\frac{1}{4}[2\times 9^2+2\times {13}^2-{10}^2]$

$=\frac{1}{4}[162+338-100]=100$

$\therefore AD=10$

$GD=\frac{1}{3}AD=\frac{10}{3}$