Question

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

Answer 1

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.