The perimeter of the rectangle is 36 cm. The sum of the lengths of its three sides is 25 cm. What is the area of this rectangle?

Let us denote the lengths of the sides of this rectangle through x and y.

According to the condition of the problem, the perimeter of this rectangle is 36 cm, therefore, we can write the following relationship:

2 * (x + y) = 36.

It is also known that the sum of the lengths of the three sides of this rectangle is 25 cm, therefore, we can write the following ratio:

x + y + x = 25.

We solve the resulting system of equations.

Subtracting the second equation from the first, we get:

2 * (x + y) – 2x – y = 36 – 25;

2x + 2y – 2x – y = 11;

y = 11 cm.

Substituting the found value y = 11 into the equation 2x + y = 25, we get:

2x + 11 = 25;

2x = 25 – 11;

2x = 14;

x = 14/2;

x = 7 cm.

Find the area of ​​the rectangle:

11 * 7 = 77 sq. cm.

Answer: the area of ​​the rectangle is 77 square meters. cm.