The length of one of the sides of the rectangle is 12 cm, and the length of its diagonal is 20 cm.

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

A diagonal divides a rectangle into two identical right-angled triangles.
Consider one of these triangles: a = 12 cm – leg, b – second leg, c = d = 20 cm – hypotenuse.
Find b by the Pythagorean theorem:
b = √ (c ^ 2 – a ^ 2);
b = √ (20 ^ 2 – 12 ^ 2) = √ (400 – 144) = √256 = 16 (cm).
The perimeter of the rectangle will be:
P = 2a + 2b;
P = 2 * 12 + 2 * 16 = 24 + 32 = 56 (cm).
Answer: P = 56 cm.