The perimeter of the rectangle is 44m, and the area is 120m ^ 2. Find all sides of the rectangle.

To calculate the sides of a rectangle, we will compose and solve a system of equations.
Let’s start by introducing two variables x m is the length of one side and y m is the length of the other.
The first equation would be:
2 (x + y) = 44;
And the second:
xy = 120.
System of equations:
x + y = 22;
xy = 120;
System:
x = 22 – y;
y (22 – y) = 120.
We solve the second equation:
22y – y ^ 2 – 120 = 0;
y ^ 2 – 22y + 120 = 0;
D = 484 – 480 = 4;
y1 = (22 + 2) / 2 = 24/2 = 12;
y2 = (22 – 2) / 2 = 20/2 = 10.
A set of systems:
System 1:
x = 22 – 12 = 10;
y = 12;
System 2:
x = 22 – 10 = 12;
y = 10.
Answer: 12 m and 10 m side lengths.