Find the diagonal of the rectangle if its perimeter is 40 cm, and the perimeter of one

Find the diagonal of the rectangle if its perimeter is 40 cm, and the perimeter of one of the triangles into which the diagonal divides the rectangle is 36 cm.

A rectangle is a quadrangle in which opposite sides are equal, and all corners are right:

AB = BC = СD = AD.

The perimeter is the sum of all its sides:

P = AB + BC + СD + AD.

AB + BC = СD + AD = R / 2;

AB + BC = СD + AD = 40/2 = 20 cm.

The diagonal of a rectangle divides it into two equal right-angled triangles.

Take, for example, the ΔABС triangle.

Since its perimeter is 36 cm, and the sum of the lengths of the sides AB and BC is 20 cm, then:

AC = 36 – 20 = 16 cm.

Answer: The length of the AC diagonal is 16 cm.