SOLUTION: A triangle has sides with lengths of 15 yards, 17 yards, and 19 yards. Is it a right triangle?

Question 1146157: A triangle has sides with lengths of 15 yards, 17 yards, and 19 yards. Is it a right triangle?

Found 3 solutions by josmiceli, Boreal, greenestamps:
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
The longest side would be the hypotenuse, so
using the Pythagorean theorem:

Now find the square of the longest side

is not true, so it can't be a right triangle

Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
square each and see if the sum of the two smaller sides equals the square of the largest side
225+289=514
19^2=361
they aren't equal
not a right triangle
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

A triangle is a right triangle if

Given that requirement, if the side lengths are integers, then c has to be odd and exactly one of a and b has to be odd.

Since the given side lengths are all odd, you can tell it is not a right triangle without doing any calculations.

Depending on your level of knowledge, you might not understand that explanation. So let's make it a little easier.

a and b are both odd, so a^2 and b^2 are both odd; then c^2 = a^2+b^2 is odd plus odd equals even. But c is odd so c^2 is odd.

So the side lengths can't all be odd integers.
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