Pythagorean Triangle/Examples/5-12-13
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Example of Primitive Pythagorean Triangle
The triangle whose sides are of length $5$, $12$ and $13$ is a primitive Pythagorean triangle.
Proof
\(\ds 5^2 + 12^2\) | \(=\) | \(\ds 25 + 144\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 169\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 13^2\) |
It follows by Pythagoras's Theorem that $5$, $12$ and $13$ form a Pythagorean triple.
Note that $5$ and $12$ are coprime.
Hence, by definition, $5$, $12$ and $13$ 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): $13$