In a right triangle, the side opposite the right angle (side c in all of the pictures in Problem A2) is called the hypotenuse.
The problems you just solved illustrate the Pythagorean theorem: In a right triangle, the square built on the hypotenuse is equal in area to the sum of the squares built on the other two sides.
Today, most people think of the theorem as stating a relationship among three numbers, a, b, and c, which represent the lengths of the sides of a right triangle.
The Pythagorean theorem is named for Pythagoras, a Greek mathematician who lived from about 569-500 B.C.E., around the same time as Lao-Tse, Buddha, and Confucius. Pythagoras was the leader of a society that would likely be considered a cult by modern standards. They studied mathematics and numerology, were very superstitious about what they ate and how they lived, and were sworn to secrecy.