This is an example of a "quantitative comparison" question the GRE would test.
Suppose the following information is known:
one side of a triangle has length 12
the perimeter of the triangle is 40
What is greater, the area of the triangle or 72?
Either (A) the area of the triangle is greater, (B) 72 is greater, (C) the two quantities are equal, or (D) the relationship cannot be determined from the information given.
Here is my strategy, which may be inefficient given time constraints of the GRE.
First, I eliminate (A) because I know I can make the area of the triangle as close to $0$ as desired, simply by making one of the angles of the triangle as close $0$ as desired. For the same reason, I can eliminate option (C).
Now I wish to show that the area of the triangle could possibly be greater than $72$. If I cannot, then choice (B) is correct. This is where I ask your help -- how can one easily find the maximum area of a triangle when only the length of one side and the perimeter is known?