The perimeter of the rectangle is 92 cm. Its width is 12 cm less than its length. Find the lengths of the sides.

The perimeter of the rectangle corresponds to the formula:

P = 2a + 2b. According to the terms of the assignment, this value for such a figure is 92 cm, and the width is 12 cm less than the length. Let’s write the equation in which we take the smallest side for “x”:

2 * (x + 12) + 2x = 92.

Let’s expand the brackets:

2x + 24 + 2x = 92.

On the left side of the equation, we perform actions with the coefficients of the variable, and transfer the known number to the right, while changing the sign in front of it to the opposite.

4x = 92 – 24 = 68.

The second factor is the quotient of the first.

x = 68: 4 = 17.

Therefore, width = 17 cm and length = 17 + 12 = 29 cm.