The perimeter of the rectangle is 36 cm and its area is 72 cm², find the lengths of the sides of the rectangle.

Let us denote the lengths of the sides of this rectangular quadrangle by x and y.

In the initial data for this task, it is reported that the sum of the lengths of all four sides of this quadrangle is 36 cm, and its area is 72 cm², therefore, the following relations take place:

2x + 2y = 36;

x * y = 72.

We solve the resulting system of equations.

Substituting into the second equation the value x = 18 – y from the first equation, we get:

(18 – y) * y = 72;

18y – y² = 72;

y² – 18y + 72 = 0;

y = 9 ± √ (81 – 72) = 9 ± √9 = 9 ± 3;

y1 = 9 + 3 = 12;

y2 = 9 – 3 = 6.

Find x:

x1 = 18 – y1 = 18 – 12 = 6;

x2 = 18 – y2 = 18 – 6 = 12.

Answer: the length of this rectangle is 12 cm, and the width is 6 cm.