This is from a practice GRE problem.
"A total of x feet of fencing is to form 3 sides of a level rectangular yard. What is the maximum area in terms of x?"
I can do the calculations and take the derivative to see that the area is maximized when the length is twice the width, thus giving $x^2/8$ as the answer. However, I do not see intuitively/geometrically why this should be true. The answer that makes the most sense to me is a square, i.e. $x^2/9$, since it at least "looks" like can start with length zero, and slowly increase until length equals width, increasing area all the time. For fencing surrounding four sides, the answer IS a square, and I don't understand the essence of the difference between these two different cases. Can anyone help me understand this problem better?