Hello Gmat_mission.

Let's see your question.

We know the following:
- The parallelogram has perimeter 16.
- The length of the base is 5.

Let "s" be the length of the other side of the parallelogram, hence we have that $$Perimeter=2base+2s\ \ \Rightarrow\ 16=2\left(5\right)+2s\ \Rightarrow\ s=3.$$ Now, the parallelogram with the largest area is the rectangle.

If we assume that the given parallelogram is a rectangle, then its area is equal to $$Area=5\cdot3=15.$$ Hence, the largest area that the given parallelogram can have is 15. This implies that the correct answer is the option A.

I hope it helps you.

Perimeter = 16 and base =5
=> 2nd side = x => 2(5 + x) = 16 => x = 3
So parallelogram sides = 5 and 3

The area of parallelogram is maximized if its a rectangle => maximum area = 5*3 =15

Answer: A <=value is greater than the maximum possible area.

Regards!