Pythagorean Triangle/Examples/4485-5852-7373

Example of Primitive Pythagorean Triangle
The triangle whose sides are of length $4485$, $5852$ and $7373$ is a primitive Pythagorean triangle.


 * 4485-5852-7373.png

It has generator $\left({77, 38}\right)$.

Proof
We have:

Hence:

It follows by Pythagoras's Theorem that $4485$, $5852$ and $7373$ form a Pythagorean triple.

We have that:

It is seen that $4485$ and $5852$ share no prime factors.

That is, $4485$ and $5852$ are coprime.

Hence, by definition, $693$, $1924$ and $2045$ form a primitive Pythagorean triple.

The result follows by definition of a primitive Pythagorean triangle.