Question

prove that the equilateral traingle described on two sides of a right angled triangle are together equal to the equilateral triangle on the hypotenuse in terms of their areas.

Answer 1

In a right angled triangle,
h²=b²+p²
√3h²/4=√3(b²+p²)/4. (multiplying both sides by √3/4)

hence area of the equilateral triangle on the hypotenuse is equal to the sum of the area of the triangle on the remaining sides