Question 74405
With any problem like thes there are Maximums and Minimums ... and when talking fencing we have to look at Perimeter first.


P1 = 1 + 1 + 39 + 39 = 80 The Area is 1 * 39 = 39
P2 = 2 + 2 + 38 + 38 = 80 The Area is 2 * 38 = 76
P3 = 3 + 3 + 37 + 37 = 80 The Area is 3 * 37 = 111
P4 = 4 + 4 + 36 + 36 = 80 The area is 4 * 36 = 144
etc .....


Notice how the area gets larger as the shape moves from a rectangle to a square.  A square will maximize the area that fencing can enclose.  With a length of 80 ft, our dimentions are 20 by 20.


P20 = 20 + 20 + 20 + 20 = 80  The Area is 20 * 20 = 400