A rectangle has two equally long sides, called length, and two equally short sides, called width. If we denote the length and the width l and w respectively we can draw the following figure.
The rectangle has a perimeter of 50 m. By adding the four sides of the rectangle the sum must equal 50. This we can write as an equation.
l+l+w+w=50⇔2l+2w=50 The rectangle's length is 3 m longer than its width. Therefore, if we subtract w from l the difference becomes 3. This gives us the following equation. l−w=3
Together, they form a system of equations.
We can find l and w by solving the system
using the elimination method. It is then necessary that one of the variable terms is eliminated when one equation is added to or subtracted from the other equation. In its current state, this won't happen. Therefore, we need to manipulate one or both equations. If we multiply Equation (II) by 2 the w-terms will have opposite coefficients.
Now we have the following system.
If we add the equations we will eliminate the w-terms.
By solving the resulting equation we find l.4l+0=56⇔l=14
To find the width of the field we can substitute 14 for l in the equation l−w=3.