Answer:
The maximum area is 18062.5 ft².
Step-by-step explanation:
Consider the provided information.
A farmer with 850 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.
The required figure is shown below.
The total length of wire is 850
The perimeter is the sum of all side which is the same as the total length of the wire, therefore
Total fence = Length of 3 parallel wall + Sides of rectangle
The area of rectangle is A=x×y
Substitute the value of y.
Now differentiate and substitute A'=0 to find the maximum.
Now substitute the value of x in
We need to find the total areas of theses configurations.
Hence, the maximum area is 18062.5 ft².