The perimeter of the rectangle is 34 cm, and one of its sides is 5 cm. Find the diagonal of the rectangle.

A rectangle is a quadrilateral in which all corners are straight, and opposite sides are parallel and equal to each other.

In order to find the length of the AC diagonal, we calculate the length of the unknown side BC.

The perimeter of a rectangle is the sum of all its sides:

P = AB + BC + CD + AD.

Since in a rectangle the opposite sides are equal:

AB = CD; BC = AD; then:

BC = AD = (P – (AB + CD)) / 2;

ВС = АD = (34 – (5 + 5)) / 2 = (34 – 10) / 2 = 24/2 = 12 cm.

To calculate the AC diagonal, consider the triangle ΔABS. This triangle is rectangular. We apply the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of the legs:

AC ^ 2 = AB ^ 2 + BC ^ 2;

AC ^ 2 = 5 ^ 2 + 12 ^ 2 = 25 + 144 = 169;

AC = √169 = 13 cm.

Answer: The length of the AC diagonal is 13 cm.