Question

How do you determine if the lengths `3, 2sqrt10, sqrt41` form a right triangle?

Answer 1

The Pythagorean Theorem finds any side of a right triangle given the two other sides. We can use this theorem to see if these lengths of sides form a right triangle.

The Pythagorean Theorem Formula is `a^2 + b^2 = c^2`, where `a` and `b` are the lengths of the sides of the triangle and `c` is the hypotenuse, or the longest side.

Therefore, we can set up an equation with the longest side being `c`:
`3^2 + (2sqrt10)^2 = (sqrt41)^2`

Simplify:
`9 + 4*10 = 41`

`9 + 40 = 41`

`49 = 41`

No, `49` does NOT equal `41`. Therefore, these lengths do not form a right triangle.