Question

If the length of a median of an equilateral triangle is x cm, then its area is

(a) x²

(b) $\frac{\sqrt{3}}{2}{x}^2$

(c) $\frac{x^2}{\sqrt{3}}$

(d) $\frac{x^2}{2}$

Answer 1

We are given the length of median of an equilateral triangle by which we can calculate its side. We are asked to find area of triangle in terms of x

Altitude of an equilateral triangle say L, having equal sides of a cm is given by, where, L = x cm

Area of an equilateral triangle, say A₁ having each side a cm is given by

Since .So

Therefore, the answer is (c).