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

1 Answer
Feb 28, 2018

Answer:

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.