The perimeter of the rectangle is 25cm. and its area is 39 cm2. find its sides.

In order to find the values of the length and width of the rectangle, we introduce the variables.

Let m be the length of the rectangle and n its width.

Based on the conditions of the problem, we will compose and solve a system of two equations:

2 * (m + n) = 25;

m * n = 39;

m + n = 12.5;

n = 12.5 – m;

Substitute the expression for the variable n into the second equation of the system:

m * (12.5 – m) = 39;

12.5 * m – m ^ 2 – 39 = 0;

2 * m ^ 2 – 25 * m + 78 = 0;

D = 625 – 624 = 1;

m1 = (25 – 1) / 4 = 6;

m2 = (25 + 1) / 4 = 6.5;

As you can see, the sides of the rectangle are 6 cm and 6.5 cm long.