# How do you determine if the lengths 9, 40, 41 form a right triangle?

Jan 6, 2017

Following the Pythagorean theorem, 9, 40, and 41 form a right triangle.

#### Explanation:

Every right triangle follows the ${a}^{2} + {b}^{2} = {c}^{2}$ format (also called the Pythagorean theorem).

$a$ and $b$ represent the two bases, which are also the two shorter sides. In this case, $a$ could represent 9 and $b$ could represent 40.

$c$ in the equation is the variable for the hypotenuse, which is the longest length in a right triangle. Plug in 41 for $c$.

So $a = 9$, $b = 40$, and $c = 41$

Now you'd test if ${9}^{2} + {40}^{2} = {41}^{2}$

We'd solve, and get $81 + 1600 = 1681$

Because $81 + 1600$ does equal $1681$, 9, 40, and 41 are the three lengths of one right triangle.