Question

A triangle has sides with lengths of 12 meters, 19 meters, and 20 meters. Is it a right triangle?

Answer 1

Answer: No it is not a right triangle.

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Work Shown:

$a = 12\\\\b = 19\\\\c = 20\\\\a^2+b^2 = 12^2+19^2 = 505\\\\c^2 = 20^2 = 400$

The values of $a^2+b^2$ and $c^2$ are not the same number

Therefore, there's no way that $a^2+b^2 = c^2$ is possible, which means we do not have a right triangle.

Put another way: since $a^2+b^2 \ne c^2$, this means we don't have a right triangle.

Refer to the converse of the pythagorean theorem for more information.

Side note: because of that same theorem, and because $a^2+b^2 > c^2$ is the case, this means we have an acute triangle based on what is shown below.