The rectangle has a perimeter of 14 dm and an area of 12 dm2. Find the sides.

To calculate the sides of a rectangle, we will compose and solve a system of equations.

Let’s start by introducing two variables x cm is the length of one side and y cm is the length of the other.

The first equation would be:

2 (x + y) = 14;

And the second:

xy = 12.

System of equations:

x + y = 7;

xy = 12;

System:

x = 7 – y;

y (7 – y) = 12.

We solve the second equation:

7y – y2 – 12 = 0;

y2 – 7y + 12 = 0;

D = 49 – 48 = 1;

y1 = (7 + 1) / 2 = 8/2 = 4;

y2 = (7 – 1) / 2 = 6/2 = 3.

A set of systems:

System 1:

x = 7 – 4 = 3;

y = 4;

System 2:

x = 7 – 3 = 4;

y = 3.

Answer: 3 in. And 3 in. Side lengths.