The perimeter of the rectangle is 22 cm, and its area is 30 cm2. Find the sides of the rectangle.

Let the sides of this rectangle be x and y.

As you know, the perimeter of a rectangle is:

P = 2 * (x + y),

and the area, respectively, is equal to:

S = x * y.

According to the condition of the problem, we compose a system of equations:

2 * (x + y) = 22,

x * y = 30.

From the first equation we get:

2 * (x + y) = 22,

x + y = 11,

y = 11 – x.

Substitute this value for y in the second equation:

x * (11 – x) = 30,

11 * x – x² = 30,

-x² + 11 * x – 30 = 0.

The discriminant of this equation is:

11² – 4 * (-1) * (-30) = 1.

The equation has the following roots:

x = (-11 + 1) / – 2 = 5 and x = (-11 – 1) / – 2 = 6.

Since y = 11 – x, we get that

if x = 5, then y = 11 – 5 = 6,

if x = 6, then y = 11 – 6 = 5.

Answer: 5 cm and 6 cm.