Question

ABC is an isosceles triangle with $AB=AC=5$ and $BC=6$. If G is the centroid of $\Delta ABC$, then AG is equal to

• A. $\frac{1}{3}$
• B. $\frac{2}{3}$
• C. $\frac{4}{3}$
• D. $\frac{8}{3}$

Answer 1

The correct option is D $\frac{8}{3}$

In an isosceles triangle, the median is perpendicular bisector of the the base. Hence, if the median cuts the base at point D then, BD = 3 cm
Using Pythagoras Theorem,
${AB}^2={BD}^2+{AD}^2$
$5^2=3^2+{AD}^2$
AD = 4 cm
The centroid divides the median in the ratio 2:1
Hence, G is the centroid than $AG:GD=2:1$
or AG = $\frac{8}{3}$