Question

In triangle ABC, G is the centroid, AB = 15 cm, BC = 18 cm and AC = 25 cm. Find GD, where D is the mid - point of BC:

• A. $\frac{1}{3}\sqrt{86}cm$
• B. $\frac{2}{3}\sqrt{86}cm$
• C. $\frac{8}{3}\sqrt{15}cm$
• D. $Noneofthese$

Answer 1

The correct option is B $\frac{2}{3}\sqrt{86}cm$

$A{B}^2+A{C}^2=2(A{D}^2+B{D}^2)$

$\therefore 225+625=2(A{D}^2+81)$
$\Rightarrow A{D}^2=344$
$\Rightarrow AD=2\sqrt{86}andGD=\frac{1}{3}AD$
$\therefore GD=\frac{2}{3}\sqrt{86}cm$