Question

Prove that the area of the equilateral triangle described on the side of a square i half the area of the equilateral triangle described on its diagnol

Answer 1

Let 'a' be the side of the square
it's diagnol is "a√2"

Area of equilateral triangle =
$\frac{ {a}^{2} \sqrt{3} }{4}$
area of 1st triangle =
$\frac{ {a}^{2} \sqrt{3} }{4}$
second is
$\frac{2 {a}^{2} \sqrt{3} }{4}$
on cancelling we get the ratio as 1 : 2
hence proved