Question

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

Options

• x²

• \[\frac{\sqrt{3}}{2} x^2\]

   

• \[\frac{x^2}{\sqrt{3}}\]

   

• \[\frac{x^2}{2}\]

   

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

`x = sqrt(3)/2 a`

`a = 2/sqrt(3) x  cm `

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

`A_1 = sqrt(3)/4 a^2`

Since `a = 2/sqrt(3) x  cm `.So

`A_1 = sqrt (3)/4 (2/sqrt(3) x )^2`

`A_1 = sqrt(3)/4 xx (4x^2)/3`

`A_1 = x^2/sqrt(3)`