Question

In an equilateral triangle, the line joining the point of intersection of medians to the base is $\frac{1}{\sqrt{3}}$ cm. Find the area of the triangle.

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

The centroid divides the median in the ratio 2:1.
So, the length of the median = $\sqrt{3}$ cm
Let the length of the side of the equilateral triangle be 'a' cm.
Length of the median of an equilateral triangle whose side length is 'a' cm = $\frac{\sqrt{3}a}{2}$ cm
$\Rightarrow$ a = 2 cm
Area of the equilateral triangle = $\frac{\sqrt{3}}{4}{a}^2$
$=\sqrt{3}c{m}^2$