Question

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

Answer 1

Area of equalateral triangle = √3s^2 / 4
But here if hight is given,
Then, Area = 1/2 * h * b
= x/2 * b
let the base be s,

Then, √3s^2 / 4 = x/2 * s
Squaring both side,
=> (√3s^2/4)^2 = (x/2)^2 *s^2
=> 3s^4/16 = x^2/4 *s^2
let s^2 be y,
Then,
=> 3y^2/16 = x^2/4* y
=>3y^2* 4 = x^2*y*16
=>12y^2 = 16x^2y
=>3y^2 = 4x^2y
=>3y = 4x^2
=>y = 4x^2/3

Then, side x side = 4x^2/3
s = 2x/√3

Area = 1/2 * x * 2x/√3
= 2x^2/2√3
= x^2/√3

MARK BRAINLIEST...