The length of one side of the rectangle is 12 cm and the length of its diagonal is 20 cm. Find the perimeter of the rectangle

1. To find the perimeter of a rectangle, define its second side.

The diagonal and the two sides of the rectangle form a right-angled triangle, in which the hypotenuse is the diagonal of the rectangle, and the legs are the known side b and the unknown side a.

By the Pythagorean theorem, we can find the second leg a of the triangle if, according to the condition of the problem, the diagonal is 20 cm and the side d is 12 cm.

a = (20 ^ 2 – 12 ^ 2) ^ 1/2 = (400 – 144) ^ 1/2 = 256 ^ 1/2 = 16 cm.

2. Find the perimeter P of the rectangle.

P = 2 * a + 2 * b = 2 * 16 cm + 2 * 12 cm = 56 cm.

Answer: The perimeter of the rectangle is 56 centimeters.