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

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.