Question

A right triangle has a hypotenuse length of 12, and one side length of 9. find the missing side length. do the side lengths form a pythagorean triple?

Answer 1

Use the Pythagorean theorem:

$a^2+b^2=c^2$

c - a hypotenuse

a, b - legs

We have: a = 9 and c = 12. Substitute:

$9^2+b^2=12^2$

$81+b^2=144$               subtract 81 from both sides

$b^2=63\to b=\sqrt{63}\\\\b=\sqrt{9\cdot7}\\\\b=\sqrt9\cdot\sqrt7\\\\ \boxed{b=3\sqrt{7}}$

A Pythagorean triple consists of three positive integers a, b and c, such that

$a^2+b^2=c^2$.

$b=3\sqrt{7}$ is not positive integer.

The sides of the triangle do not form a pythagorean triple.