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

1. Let one side of the rectangle be x, then the other is y.

2.The perimeter is equal to the sum of all sides, since 2 sides are the same, the equation will look like:

2x + 2y = 22.

3. The area of ​​a rectangle is equal to the product of its sides, the equation will look like:

x * y = 30.

4. Let’s solve the system of equations. From the first equation, we express x:

x = (22 – 2y): 2;

x = 11 – y.

5. Substitute the value of x in the second equation:

(11 – y) * y = 30;

11y – y ^ 2 = 30;

-y ^ 2 + 11y – 30 = 0.

Let’s find the discriminant:

D = b ^ 2 -4ac = 121 – 120 = 1.

D> 0, the equation has 2 roots:

x1 = (-11 + 1) / (-2) = 5;

x2 = (-11 – 1) / (-2) = 6.

Answer: One side of the rectangle is 5 cm, the other side is 6 cm.