The perimeter of the rectangle is 14 and its area is 12. Find the lengths of the sides of the rectangle.

Let’s write down what is given to us in the condition:

We are given a rectangle with area S = 12 and perimeter P = 14.

We need to find the sides of the given rectangle a -? b -?

To begin with, we write down the formula for the perimeter of a rectangle and derive the value a + b from there:

P = 2 * (a + b)

a + b = P ÷ 2

a + b = 14 ÷ 2

a + b = 7,

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

S = a * b

a * b = 12,

We see that we have obtained a system of equations that can be solved by the selection method:

a + b = 7

a * b = 12,

The numbers satisfying both equalities are 4 and 3.

Answer: the sides of the rectangle are 4 and 3, respectively.