G is the centroid of the equilateral ΔABC. If AB = 10 cm then length of AG is ?

Answer: Option B

According to question,

Given :
AB = BC = CA = 10 cm
G = Centroid
AG = 2 units
GD = 1 unit
AD = 3 units = Height
As we know that the height of the equilateral triangle is
$$\begin{array}{rl}& =\frac{\sqrt{3}}{2}\times 10=5\sqrt{3}\\ & \therefore 3\text{units}=5\sqrt{3}\\ & 1\text{unit}=\frac{5\sqrt{3}}{3}\\ & 2\text{units}=\frac{5\sqrt{3}}{3}\times 2\\ & 2\text{units}=\frac{10\sqrt{3}}{3}\\ & \therefore \text{AG}=\frac{10\sqrt{3}}{3}cm\end{array}$$