A farmer has 120 feet of fencing which she plans to use
to fence in a plot of land for a
pig pen. If she chooses to
enclose a plot along the broad
side of her barn, what is the
largest area that can be
enclosed? (Note The side along
the barn will not require
fencing.)

If the barn is at least 60 feet long, the farmer can make the pen 60 by 30. That will result in an area of 1800 square feet.

Step-by-step explanation: You can try any combinations of dimensions that add up to 2w + 1L = 120

For example:

2(20) + 80 = 120   Area = 20 × 80 = 1600  square feet

2(25) + 70 = 120   Area = 25 × 50 =  1750  square feet  increasing

2(30) + 60 = 120  Area = 80 × 40  = 1800 square feet  = MAX

2(35) + 50 = 120 Area =  35 × 50 =  1750  sq ft  decreasing again