# The rectangle has a perimeter of 26 cm and an area of 42 cm2. Find the sides of the rectangle.

The solution of the problem.

1. Let’s denote by x one side of the rectangle, and by y the other side of the rectangle.

2. The perimeter of the rectangle is 2 * (x + y).

3. The area of the rectangle is xy.

4. Let’s compose and solve the system of equations.

2 * (x + y) = 26;

xy = 42;

From the first equation of the system, we express y through x.

x + y = 13;

y = 13 – x;

Substitute the value for y in the second equation.

x * (13 – x) = 42;

x ^ 2 – 13x + 42 = 0;

D = 169 – 168 = 1;

The equation has 2 roots x1 = 6 and x2 = 7.

Both roots satisfy the condition of the problem.

5. Find y.

y = 13 – x;

y1 = 13 – 6 = 7;

y2 = 13 – 7 = 6;

6. In both cases, one side of the rectangle is 6 cm and the other 7 cm.

Answer. The lengths of the sides of the rectangle are 6 cm, 7 cm.