Chapter 10 - Radical Expressions and Equations - 10-1 The Pythagorean Theorem - Practice and Problem-Solving Exercises - Page 617: 31

Pythagorean Triple.

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 a Pythagorean Triple, we plug them into the Pythagorean Theorem: $13^{2} + 84^{2} = 85^{2} \\\\ 7225=7225$ This is true, so it is a Pythagorean Triple.