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=√(63)\\\\b=√(9\cdot7)\\\\b=\sqrt9\cdot\sqrt7\\\\ \boxed{b=3√(7)}`

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

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

`b=3√(7)` is not positive integer.

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