The perimeter of the rectangle is 42 cm and the area is 108 cm2. Find the length and width of the rectangle.

We are given a rectangle with an area of S = 108 cm² and a perimeter of P = 42 cm.

Need to find the sides of the given rectangle a -? b -?

First, we write down the formula for the perimeter of the rectangle and derive the value of the side a + b from the formula:

P = 2 * (a + b)

a + b = P ÷ 2

a + b = 42 ÷ 2

a + b = 21,

Now let’s write the formula for the area of a rectangle:

S = a * b

a * b = 108,

We have a control system:

a + b = 21

a * b = 108

Using the selection method, we find numbers satisfying both equalities:

12 + 9 = 21

12 * 9 = 108.

Answer: the sides of the rectangle are 12 and 9 cm.