Pythagorean Triple/Examples/5, 12, 13

Example of Pythagorean Triple

The triple $\tuple {5, 12, 13}$ forms a Pythagorean triple which is also a primitive Pythagorean triple.


Proof

\(\ds 5^2 + 12^2\) \(=\) \(\ds 25 + 144\)
\(\ds \) \(=\) \(\ds 169\)
\(\ds \) \(=\) \(\ds 13^2\)


Hence $\tuple {5, 12, 13}$ is a Pythagorean triple by definition.

We also have that $5 \perp 12$, demonstrating that $\tuple {5, 12, 13}$ is a primitive Pythagorean triple.

$\blacksquare$


Sources

  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Pythagorean triple
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