Find the diagonal of the rectangle if one of its sides = 8 cm and Perimeter = 46 cm.

In order to find the length of the diagonal of a rectangle, we will consider a right-angled triangle formed by the two sides of the rectangle and the diagonal.

The diagonal in the triangle will be the hypotenuse, and the sides of the rectangle will be the legs.

Let’s start by finding the second side of the rectangle. Let’s apply the formula for calculating the perimeter of a rectangle.

P = 2 (a + b);

2 (a + 8) = 46;

a + 8 = 23;

a = 23 – 8;

a = 15.

Let’s apply the Pythagorean theorem to find the hypotenuse:

c ^ 2 = a ^ 2 + b ^ 2;

c = √ (15 ^ 2 + 8 ^ 2) = √ (225 + 64) = √289 = 17 cm.