Question

Using the Pythagorean Theorem, is a triangle with side lengths `\sqrt 2, \sqrt3, and \sqrt 5` ft a right triangle?

Answer 1

Yes

Explanation:

The theorem states that the length of the sides `a, b and c` of a right-angled triangle is related as follows: `a^2+b^2=c^2` where `c` is obviously the hypotenuse.

We can use the formula in reverse to check if the given side lengths form a right triangle or not.

If we assume `sqrt(5)` to be the hypotenuse of this triangle (by common sense - it is the longest side), we get `sqrt(2)^2+sqrt(3)^2=sqrt(5)^2`

But since `sqrt(x)^2` is `x` for positive `x`, we can simplify it to: `2+3=5`.

And that is true indeed.