The perimeter of the rectangle is 26 cm, and its area is 36 cm2. find the lengths of the sides of the rectangle

In order to find the length and width of the rectangle, we compose and solve a system of equations.

Let us denote by variables x and y the length and width of the rectangle, respectively.

Formula for finding the perimeter P = 2 (a + b);

The formula for finding the area: S = a * b.

System of equations:

2 (x + y) = 26;

xy = 36.

System of equations:

x + y = 13;

xy = 36;

System of equations:

x = 13 – y;

(13 – y) y = 36.

We solve the equation:

13y – y2 – 36 = 0;

y2 – 13y + 36 = 0;

D = 169 – 144 = 25;

y1 = (13 + 5) / 2 = 18/2 = 9;

y2 = (13 – 5) / 2 = 8/2 = 4.

A set of systems:

System 1:

x = 13 – y = 13 – 9 = 4;

y = 9.

System 2:

x = 13 – y = 13 – 4 = 9;

y = 4.

Answer: 9 and 4 cm.