The maximum amount of area that can be enclosed by a set length of fence is always a perfect square. So the ratio of length to width should be 1:1.
This may seem silly but consider if you had only 8 feet of fencing. The best possible option would be to have 4 sides of 2 feet a piece for a total of 4 square feet.
2* 2 = 4
Any other option gets increasingly smaller. For instance, if we had two sides of 3 and two sides of 1, that only gives us 3 square feet.
3*1 = 3
Then if we make two sides 3.5 feet and another .5 feet it gets even smaller.
3.5*.5 = 1.75
This shows us a trend and allows us to know that a square is the maximum area.
