I've been working on a problem set of math problems lately, but I've come across some difficulty with the problem below.
The dimensions of a rectangular piece of paper ABCD are AB=10 and BC=9. It is folded so that corner D is matched with a point F on edge BC. The lengths of EF, EC, and FC are all determined by the length of DE. Let DE=x.
a. Write and equation for the area of EFC in terms of x.
b. Find the value for x that maximizes the area of EFC.
I understand that we could use the Pythagorean theorem, but I'm not quite sure how to make it work. Additionally, if the answer involves calculus, inform me, as I will be unable to work with that due to my lack of understanding of that subject matter. Also, providing the equations for it would be especially helpful.