The perimeter of the rectangle is 28 m, and its area is 40 m2, find the sides of the rectangle through the system.

The side of a rectangle can be expressed as the ratio of the area to the other side. Because according to the condition of the problem, the area is 40 m2, and if we denote by x cm – the width of the rectangle, then 40 / x m – the length of this rectangle. Perimeter P = (a + b) * 2. If the perimeter is 28 meters, substitute x and 40 / x in the formula:

(40 / x + x) * 2 = 28

40 / x + x = 14

40 + x ^ 2 – 14x = 0

x ^ 2 – 14x + 40 = 0

D = b2 – 4ac

D = 196 – 4 * 40 = 36.

x = (-b ± √D) / 2a

x = (14 ± 6) / 2

x1 = 10, x2 = 4.

Answer: the sides of the rectangle are 4 cm and 10 cm.