The area of the rectangle is 14 cm2 and the perimeter is 18 cm. Find the measurements of the rectangle.

Let’s define the semi-perimeter of the rectangle:

18/2 = 9.

Let’s denote the first dimension of the rectangle through the variable x

Then the second dimension of the rectangle will be (9 – x).

Knowing that the area of the rectangle is 14 cm2, we draw up an equation and determine the lengths of its sides:

x (9 – x) = 14;

9x – x ^ 2 = 14;

x ^ 2 – 9x + 14 = 0;

D = 81 – 4 * 14 = 25 = 52;

x1 = (9 – 5) / 2 = 2;

x2 = (9 + 5) / 2 = 7.

Answer: The length of the first dimension of the rectangle is 2 centimeters, the length of the second dimension is 7 centimeters.