An equilateral triangle is built on the side of the square, the diagonal of the square = 15 cm

An equilateral triangle is built on the side of the square, the diagonal of the square = 15 cm Find the perimeter of the triangle.

Since the quadrangle ABCD, by condition, is a square, then AB = BC = CD = AD. Then, in a right-angled triangle ACD, we define, according to the Pythagorean theorem, the legs AD and CD, which are the sides of the square.

AC ^ 2 = AD ^ 2 + CD ^ 2 = 2 * AD ^ 2.

15 ^ 2 = 2 * AD ^ 2.

AD = √ (225/2) = 15 / √2 = 15 * √2 / 2 = 7.5 * √2 cm.

Then, ВС = ВK = СK = АD = 7.5 * √2 cm.

Determine the perimeter of the triangle ВСK.

P = 3 * BC = 3 * 7.5 √2 = 22.5 * √2 cm.

Answer: Rvsk = 22.5 * √2 cm.