The perimeter of the rectangle is 16 cm, and its area is 15 cm2. Find the lengths of the sides of this 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) = 16;

xy = 15;

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

x + y = 8;

y = 8 – x;

Substitute the value for y in the second equation.

x * (8 – x) = 15;

x ^ 2 – 8x + 15 = 0;

D = 64 – 60 = 4;

The equation has 2 roots x1 = 3 and x2 = 5.

Both roots satisfy the condition of the problem.

5. Find y.

y = 8 – x;

y1 = 8 – 3 = 5;

y2 = 8 – 5 = 3;

6. In both cases, one side of the rectangle is 3 cm and the other 5 cm.

Answer. The lengths of the sides of the rectangle are 3 cm, 5 cm.