Question

In the Pythagorean Theorem why do we use the area of the legs if they were squares to solve for the hypotenuse and not the legs' lengths.

Answer 1

http://www.mathsisfun.com/pythagoras.html

Answer 2

Yup. What sunnyshine said.

Answer 3

... or posted :P

Answer 4

There are over 500 different proofs of the Pythagorean Theorem. There are some that appear to use these "areas". Whatever they are, they are just proofs. They are not written in stone and requiring us to worship them. If it helps you not to think of the area, then don't. The relationship is the same.