Let the three sides be $a-d,$ $a,$ and $a+d.$ Because of the Pythagorean Theorem,
$$(a-d)^2 + a^2 = (a+d)^2$$
This can be simplified to
$$a(a-4d) = 0.$$
So, $a$ is a multiple of $4d$ and the triangle has sides $3d, 4d, 5d.$ We check the answer choices for anything divisible by 3, 4, or 5. The only one that works is 81, which is divisible by 3.
The answer is $\textbf{(C)}\ 81.$
-edited by coolmath34