дано: прямоугольник периметр равен 22 площадь равна 30 см² найти стороны прямоугольника

Let's assume the length of the rectangle is x cm and the width is y cm.

The perimeter of a rectangle is given by 2(length + width). From the given information, we can write the equation:

2(x + y) = 22

Simplifying the equation, we get:

x + y = 11 ----- Equation 1

The area of a rectangle is given by length * width. From the given information, we can write the equation:

x * y = 30

Now, we have a system of equations. We can solve it using different methods like substitution or elimination.

Let's use substitution to solve it.

From Equation 1, we have:

x = 11 - y

Substituting this value in the second equation:

(11 - y) * y = 30

Expanding and simplifying:

11y - y^2 = 30

Rearranging the equation:

y^2 - 11y + 30 = 0

This is a quadratic equation. We can solve it by factoring or using the quadratic formula.

Factoring the equation, we get:

(y - 5)(y - 6) = 0

So, either y - 5 = 0 or y - 6 = 0

If y - 5 = 0, then y = 5 If y - 6 = 0, then y = 6

Substituting these values back into Equation 1, we can find the corresponding values of x:

When y = 5: x + 5 = 11 x = 11 - 5 x = 6

When y = 6: x + 6 = 11 x = 11 - 6 x = 5

Therefore, the sides of the rectangle are 6 cm and 5 cm (or vice versa).