Answer:
Step-by-step explanation:
Let the dimensions of the wall be x and y
Since only three of the sides will require fencing
Perimeter=2x+y (where y is the side opposite the wall)
The farmer has 132 feet of fencing
Therefore: Perimeter=132 feet
2x+y=132
y=132-2x
Area of the enclosure, A(x,y)=xy
Substituting y=132-2x into A(x,y)
Area, A(x)=x(132-2x)
To determine the largest area the farmer can enclose, we maximize A(x) by finding its derivative and solving for its critical point.
Set A'(x)=0
132-4x=0
4x=132
x=33 feet
Recall: y=132-2x
y=133-2(33)= 66 feet
Therefore, the largest area the farmer can enclose is that of an enclosure which has dimensions 33 X 66ft.
Maximum Area= 1387 square feet :)
