Question

A triangle has sides with lengths of 13 feet, 16 feet, and 4 feet. Is it a right triangle?

Answer 1

well, a right-triangle will have one angle that is 90°, and using the pythagorean theorem, we also know that the longest side is really the root of the sum of the square of the other two.  After all that mouthfull let's check

$\stackrel{longest}{16}~~ = ~~\sqrt{\underset{short}{13^2}~~ + ~~\underset{short}{4^2}}\implies 16=\sqrt{169+16} \\\\\\ 16=\sqrt{185}\implies 16^2=185\implies 256~~ \ne ~~185\qquad \leftarrow \textit{nope, it isn't}$