Prove that the area of an equilateral triangle described on the diagonal of a square is twice the area of an equilateral triangle described on its side.
Open in App
Solution
Let the side of Square be a
Diagonal a√2
Area of equilateral triangle on its Diagonal is √34(a√2)2√32a2⋯(1)
area of equilateral triangle in its side is √34a2⋯(2)