Chapter 10 - Radical Expressions and Equations - 10-1 The Pythagorean Theorem - Practice and Problem-Solving Exercises - Page 603: 24

This is not true, so it cannot be a right triangle.

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.