Answer
It cannot be a right triangle.
Work Step by Step
The Pythagorean Theorem states that for a right triangle, $a^{2} +b^{2} = c^{2}$. In order to figure out if these sides can be the sides of a right triangle, we plug them into the Pythagorean Theorem:
$12^{2} + 60^{2} = 61^{2} \\\\ 3744=3721$
This is not true, so it cannot be a right triangle.