Which of the following best describes what is unique about Pythagorean triples?

• A. They are sets of three numbers that can only be used in equilateral triangles.
• B. They are sets of three positive integers that satisfy the equation $a^2+b^2=c^2$.
• C. They are sets of three integers where the sum of any two equals the third.
• D. They are sets of three real numbers that form the sides of any triangle.

Answer: (B)

Verified step by step guidance

1. Understand that Pythagorean triples are related to the Pythagorean theorem, which applies to right-angled triangles.
2. Recall the Pythagorean theorem formula: \(a^{2} + b^{2} = c^{2}\), where \(a\) and \(b\) are the legs of a right triangle and \(c\) is the hypotenuse.
3. Recognize that Pythagorean triples are sets of three positive integers \((a, b, c)\) that satisfy this equation exactly.
4. Note that these triples are unique because all three numbers are integers, not just any real numbers, and they specifically satisfy the Pythagorean equation.
5. Understand that Pythagorean triples do not apply to equilateral triangles or any triangle, but specifically to right triangles with integer side lengths.