Question

Prove that area of the equilateral triangle described on the side of a square is half of the area
of the equilateral triangle described on its diagonal.

Answer 1

Let the side of square be a.
Area of equilateral triangle on the side = √3/4 a^2
Area of equilateral triangle on the diagonal = √3/4 (√2 a^2) since diagonal of a square is √2 a.
On solving, we get it as twice of the first result.

Answer 2

plz refer to this attachment