Legs of Pythagorean Triangle used as Generator for another Pythagorean Triangle/Examples

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Examples of Legs of Pythagorean Triangle used as Generator for another Pythagorean Triangle

$3-4-5$ Triangle

The $3-4-5$ triangle has hypotenuse $5$.

3-4-5.png


By Solutions of Pythagorean Equation, the Pythagorean triangle $P_2$ formed by the generator $\left({4, 3}\right)$ is:

\(\displaystyle P_2\) \(=\) \(\displaystyle \tuple {2 \times 4 \times 3, 4^2 - 3^2, 4^2 + 3^2}\)
\(\displaystyle \) \(=\) \(\displaystyle \tuple {24, 7, 25}\)

It is observed that $25 = 5^2$.

7-24-25.png