Find the diagonal of the rectangle if one side is 8cm and the perimeter is 46cm.

The diagonal of a rectangle splits it into two equal right-angled triangles, in which:

AB = CD;

BC = AD,

and the AC diagonal is common.

Since the sum of all sides of the rectangle is 46 cm, the sum of the sides AB and BC is equal to half of this perimeter:

AB + BC = P / 2;

AB + BC = 46/2 = 23 cm.

Since the side AB is 8 cm, then:

BC = 23 – 8 = 15 cm.

To calculate the AC diagonal, we apply the Pythagorean theorem:

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

AC ^ 2 = 8 ^ 2 + 15 ^ 2 = 64 + 225 = 289;

AC = √289 = 17 cm.

Answer: the AC diagonal is 17 cm.