This all sounds very nice, but what's the use of this?

One thing you
can do with the Pythagorean thereom is to calculate the length of any side
of a right triangle if you know the other two.

For example, you have a right
triangle with one leg measuring 3 inches and another leg measuring 4 inches.
Can you find the size of the hypotenuse without drawing and measuring?

Did you get an answer? Here's my solution: The square which is along the
side which has a length of 4 has an area of 16. (To get the area of a rectangle
multiply the width by the height. A square is as wide as it is long. So multiply
4 by 4 which equals 16.) The area of the other square is 9 (3×3). This adds up to
an area of 25. So which number can you multiply by itself to give
25? 5! The third side (the hypotenuse) therefore has a length of 5.

In this example all sides have lengths which are whole numbers. Can you find any
other triangles where this is the case?