The perimeter of the rectangle is 32 cm. The length of one side is 2 cm less than the length of the other.

The perimeter of the rectangle is 32 cm. The length of one side is 2 cm less than the length of the other. Find the area of a rectangle.

P = 32 cm.

a (length) = x + 2 cm.

b (width) = x cm.

S =?.

1) The perimeter of the rectangle is calculated by the formula:

P = 2a + 2b.

Let’s write the equation according to the task condition:

2 * (x + 2) + 2 * x = 32.

Let’s expand the brackets:

2x + 4 + 2x = 32.

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

4x = 32 – 4 = 28.

x = 28: 4 = 7.

Therefore, 7 cm is the width of the rectangle, and 7 + 2 = 9 cm is its length.

2) S = a * b = 7 * 9 = 63 cm² is the area of a rectangle.