Question

find out the area of an equilateral triangle whose altitude is square root of 6?

Answer 1

Let each side of the triangle be 2x then altitude bisect the side with two parts x and x now by pythagoreous theorem (2x)^2 = x^2 + root 6^2 => 4x^2 -x^2 = 6 => 3x^2=6 => x^2 = 2 => x = root2 and each side = 2root 2 now area of triangle = 1/2 base *height = 1/2 x 2 root2 x root 6 = root 12 answer