To determine the best description for sets of three whole numbers [tex]\( (a, b, \)[/tex] and [tex]\( c) \)[/tex] that satisfy the equation [tex]\( a^2 + b^2 = c^2 \)[/tex], we need to understand each of the given options:
A. Perfect squares: Perfect squares are numbers that can be expressed as the product of an integer with itself (e.g., [tex]\( 1, 4, 9, 16, \)[/tex] etc.). This option does not describe sets of three numbers but describes individual numbers.
B. Prime numbers: Prime numbers are numbers greater than 1 that have no positive divisors other than 1 and themselves (e.g., 2, 3, 5, 7, 11, etc.). This option talks about individual numbers with specific divisibility properties, not about sets of three numbers.
C. Pythagorean triples: Pythagorean triples are sets of three whole numbers [tex]\( (a, b, c) \)[/tex] such that [tex]\( a^2 + b^2 = c^2 \)[/tex]. This definition directly matches the description in the question.
D. The Pythagorean theorem: The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem provides the foundation for the relationship [tex]\( a^2 + b^2 = c^2 \)[/tex], but it describes a geometric principle, not a set of numbers.
Given the choices, the best description for sets of three whole numbers [tex]\( (a, b, c) \)[/tex] that satisfy the equation [tex]\( a^2 + b^2 = c^2 \)[/tex] is:
C. Pythagorean triples
