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

To solve this problem, we introduce two conditional variables “X” and “Y”, through which we denote the sides of the rectangle.

Then, based on the data of the problem, we compose the following equations:

1) (X + Y) x 2 = 36;

2) 2X + Y = 25.

Solving a system of two equations with two unknowns, we obtain Y = 25 – 2X.

Substituting Y into the first equation, we get X + 25 – 2X = 18 or X = 7 centimeters.

Therefore, Y will be equal to 25 – 2 x 7 = 11 centimeters.

Then, the area of the rectangle will be 7 x 11 = 77 cm2.

Answer: the area of the rectangle is 77 cm2.