# ABCD-square. MNKL-midpoints of the sides of the square. Find the perimeter of MNKL if the diagonal of the square = 10 cm.

In a right-angled triangle, where the diagonal of the square ABCD is the hypotenuse, and the two sides of the square are the legs, we write down the Pythagorean theorem:

d² = a² + a² = 2a² = 10² = 100;

a² = 50

a = √50 (cm) – side of the square ABCD.

√50 / 2 (cm) – half of the side of the square ABCD.

Consider a right-angled triangle in which the legs are equal to half of the side of the square ABCD, and the hypotenuse is the side of the square MNKL, we denote it as a2.

a2² = (√50 / 2) ² + (√50 / 2) ² = 100/4 = 25;

a2 = 5 (cm).

P MNKL = 4 * a2 = 20 (cm).

You can solve it in another way, depending on what topic you are going through.

In triangle ABC, the side of the square MNKL is the middle line, which means it is equal to half of the AC, i.e. 5 cm.

P MNKL = 4 * 5 = 20 (cm).

Answer: The perimeter of the MNKL square is 20 cm.