The perimeter for this case is given by:
Substituting values we have:
The area is given by:
Writing the area based on a variable we have:
We derive the area to obtain the maximum of the function:
We equal zero and clear x:
Then, the other dimension is given by:
Finally the maximum area is:
Answer:
The length and width of the plot that will maximize the area are:
The largest area that can be enclosed is:
