# 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. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.