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Work Shown:
[tex]a = 12\\\\b = 19\\\\c = 20\\\\a^2+b^2 = 12^2+19^2 = 505\\\\c^2 = 20^2 = 400\\\\[/tex]
The values of [tex]a^2+b^2[/tex] and [tex]c^2[/tex] are not the same number
Therefore, there's no way that [tex]a^2+b^2 = c^2[/tex] is possible, which means we do not have a right triangle.
Put another way: since [tex]a^2+b^2 \ne c^2[/tex], 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 [tex]a^2+b^2 > c^2[/tex] is the case, this means we have an acute triangle based on what is shown below.
