A Farmer wants to construct a fence. The area that he is going to enclose is rectangular, but one of the sides is a river (assumed to be straight). If he has 120 m of fence, what is the maximum surface that he can enclose?© BrainMass Inc. brainmass.com February 24, 2021, 2:09 pm ad1c9bdddf
The rectangle is characterized by two numbers a and b (the lengths of the distinct sides). Suppose that the side by the river is of length a, hence the amount of fence that the farmer needs is:
a + b + b = 120 m.
The area enclosed by the rectangle is ...
This shows how to maximize area given a perimeter.