The perimeter of a rectangle is 72 cm, and the perimeter of a rectangle composed

The perimeter of a rectangle is 72 cm, and the perimeter of a rectangle composed of three such rectangles is 120 cm. Find the sides of the rectangle.

We denote the sides of the rectangle by X and Y.

Then its perimeter is: P1 = 2 * X + 2 * Y = 72.

Since when three such perimeters are added, one side does not change, and the second increases by three, the perimeter of three folded such rectangles will be equal to:

P2 = 6 * X + 2 * Y = 120.

Let us solve the system of two equations by the substitution method.

X = (72 – 2 * Y) / 2 = 36 – Y.

6 * (36 – Y) + 2 * Y = 120.

216 – 6 * Y + 2 * Y = 120.

4 * Y = 96.

Y = 96/4 = 24.

X = 36 – 24 = 12.

Answer: The sides of the rectangle are 12 and 24 cm.