The perimeter of the rectangle is 22 cm, and its area is 28 cm2 Find the sides of the rectangle.

1. Let a and b be the sides of the rectangle.

2. Let’s compose a system of equations in which the first equation will express the perimeter of the rectangle, and the second – the area.

{2 • (a + b) = 22,

{a • b = 28.

3. In the first equation, divide both sides by 2.

{a + b = 11,

{a • b = 28.

4. Let us express one of the sides in the first equation, substitute it into the second and solve it.

a = 11 – b,

(11 – b) • b = 28,

11b – b ^ 2 = 28,

b ^ 2 – 11b + 28 = 0,

b1 = 4, b2 = 7.

Let us express a in terms of the obtained values of b.

a1 = 11 – 4 = 7,

a2 = 11 – 7 = 4.

Answer: The width of the rectangle is 4 and the length is 7.