If you draw a right-angled triangle, the side which doesn't touch the right angle is called the hypotenuse. According to Pythagoras' theorem, the length of this side squared is equal to the square of the other two sides.

To test this out, draw two lines which cross at a right angle. Mark a point 12 centimetres (or inches, if you prefer) along one line, and mark another point 5 centimetres along the other. Draw a line between the two points.

If you measure the line, it should be 13 centimetres long.

12 squared (144) + 5 squared (25) = 13 squared (169)

I chose this example because all lengths are whole numbers (integers), but it works for any lengths, whether integers or not, as long as the triangle is right-angled.

If you can combine 3 integers to make a right-angled triangle, as we just did with 5, 12 and 13, you have a Pythagorean triple. Another common example is 3, 4 and 5. The largest number, of course, is the biggest side, the hypotenuse.

Learn more about this author, Jon Eccles.
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