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Pythagorean Triples

Three whole numbers $a,b,c$ which satisfy the equation of the Pythagorean Theorem ( $a^2+b^2=c^2$ ) are called Pythagorean triples . A few of the smallest ones are shown in the table below. Each Pythagorean Triple corresponds with a right triangle whose side lengths are in whole-number ratios.

Note that once you have one Pythagorean triple, you can get many more: just multiply all $3$ numbers by a constant. For instance, from $3,4,5$ , we get the family of triples:

$\begin{array}{l}3,4,5\\ 6,8,10\\ 9,12,15\\ 12,16,20\\ 15,20,25\end{array}$

etc.