A farmer is building a fence to enclose a rectangular area against an existing wall. Three of the sides will require fencing and the fourth wall already exists. If the farmer has 132 feet of fencing, what is the largest area the farmer can enclose?

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 :)

step-by-step explanation:

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hj=3x+20

ji=15x-64