# The perimeter of the rectangle is 56 cm. One of its sides is 16 cm. Calculate the length of the diagonals of the rectangle.

October 4, 2021 | education

| The opposite sides of the rectangle are equal to each other, which means that the sum of two adjacent sides is equal to half of the perimeter:

a + b = P / 2;

a + b = 56/2 = 28 cm.

Let by condition a = 16 cm, then b = 28 – 16 = 12 cm.

The diagonal of a rectangle and two adjacent sides form a right-angled triangle, in which the diagonal is the hypotenuse, the sides are the legs. Therefore, by the Pythagorean theorem:

d ^ 2 = a ^ 2 + b ^ 2 = 16 ^ 2 + 12 ^ 2 = 256 + 144 = 400 = 202;

d = 20.

The diagonals of the rectangle are equal to each other, which means d1 = d2 = 20 cm.