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): $13$