Problema Solution
A rancher has 800 feet of fencing to put around a rectangular field and then subdivide the field into 2 identical smaller rectangular plots by placing a fence parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms.
Answer provided by our tutors
A maximized area is a square. Let 'x' represent the side of a square, then the length of fence required on each side is:
4x+3x=800
x=800/7
So the rectangle will be 800/7 by 1600/7.
So over 685 feet of fence is used for the outer perimeter and under 115 feet is used for the dividing side:
(2*1600)/7+(2*800)/7
685.7