The area of an equilateral triangle is equal to the area of a square with diagonal  20cm . The side of the triangle is

The area of an equilateral triangle is given by the formula: A = (s^2 * sqrt(3)) / 4, where s is the side of the triangle.

The area of a square is given by the formula: A = s^2, where s is the side of the square.

However, in this case, we are given the diagonal of the square, not the side. The diagonal of a square is related to the side by the formula: d = s * sqrt(2), where d is the diagonal and s is the side.

So, if the diagonal of the square is 20 cm, we can find the side of the square by rearranging the formula to solve for s: s = d / sqrt(2) = 20 / sqrt(2) = 20 * sqrt(2) / 2 = 10 * sqrt(2) cm.

Since the area of the square is equal to the area of the equilateral triangle, we can set the two area formulas equal to each other and solve for the side of the triangle:

(s^2 * sqrt(3)) / 4 = (10 * sqrt(2))^2 s^2 * sqrt(3) = 400 * 2 s^2 * sqrt(3) = 800 s^2 = 800 / sqrt(3) s = sqrt(800 / sqrt(3)) s = sqrt(800 * sqrt(3) / 3) s = 20 * sqrt(sqrt(3) / 3) cm

So, the side of the equilateral triangle is approximately 20 * sqrt(sqrt(3) / 3) cm.