A rectangle is a quadrilateral having opposite sides equal
The perimeter is given by the formula
[tex]2(L+B)[/tex]
The area is given by
[tex]L\times B[/tex]
To get the maximum area
If the fence is rectangular, it will have the largest possible area when the length equals the width. In order to have a perimeter of 480 feet, that means that each side needs to be 120 feet.
For any given rectangle, the area is maximized when all the sides are equal
Thus, the maximum area is
[tex]120ft\text{ by 120ft}[/tex]
Thus, the length is
[tex]\begin{gathered} \text{Length}=120ft \\ \text{Width}=120ft \end{gathered}[/tex]
