112 feet of fence is the length of the fencing. The area of a rectangle is length times width. The perimeter of a rectangle is the sum of twice the length and twice the width.
Let length = x
Let width = y
Use these variables to create equations.
2(x + y) = 112 eq1
x + y = 56 eq1
Area = xy eq2
Substitute eq1 into eq2 to get a function area in terms of only x and y.
Area = x(56 - x)
Area = -x2 + 56x
The area represents a parabola that opens downward. What you need to do is find the vertex of this parabola.
Find the x-coordinate of the vertex using this formula:
x = -b / (2a)
a = -1
b = 56
Plug in these values into the formula. Then evaluate the area at that x-coordinate. That will be your maximum area.