# Legs of Pythagorean Triangle used as Generator for another Pythagorean Triangle/Examples/3-4-5

## Example of Legs of Pythagorean Triangle used as Generator for another Pythagorean Triangle

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

By Solutions of Pythagorean Equation, the Pythagorean triangle $P_2$ formed by the generator $\tuple {4, 3}$ 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 $25 = 5^2$.