Pythagorean Triangle/Examples/7-24-25

Example of Primitive Pythagorean Triangle

The triangle whose sides are of length $7$, $24$ and $25$ is a primitive Pythagorean triangle.



Proof

\(\ds 7^2 + 24^2\) \(=\) \(\ds 49 + 576\)
\(\ds \) \(=\) \(\ds 625\)
\(\ds \) \(=\) \(\ds 25^2\)

It follows by Pythagoras's Theorem that $7$, $24$ and $25$ form a Pythagorean triple.


Note that $7$ and $24$ are coprime.

Hence, by definition, $7$, $24$ and $25$ form a primitive Pythagorean triple.

The result follows by definition of a primitive Pythagorean triangle.

$\blacksquare$


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $13$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $13$
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