Using calculus, A land owner has 2000 meters of fencing and wishes to fence off a rectangular field, what are the dimensions of the fencing that encloses the maximum area ?

Answer 1

The rectangle with the largest area for a given perimeter is a square.

The equations you need to show this are:

2(L+W)=2000

Area = LW

Substitute from the first equation into the second.

Then differentiate Area with respect to the remaining variable. Set the derivative equal to 0 and solve for the variable (L or W).