Final answer:
Pythagorean Triples are sets of three whole integers that fit the Pythagorean Rule. To determine whether a set of numbers is a Pythagorean Triple, we need to check if the equation a² + b² = c² holds true for that set. Among the given sets, a), b), c), and e) are Pythagorean Triples.
Step-by-step explanation:
Pythagorean Triples are sets of three whole integers that fit the Pythagorean Rule, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the two legs (a and b). To determine whether a set of numbers is a Pythagorean Triple, we need to check if the equation a² + b² = c² holds true.
a) 8, 15, 17:
Yes, this set of numbers is a Pythagorean Triple because 8² + 15² = 64 + 225 = 289 = 17².
b) 15, 20, 25:
Yes, this set of numbers is a Pythagorean Triple because 15² + 20² = 225 + 400 = 625 = 25².
c) 20, 48, 52:
Yes, this set of numbers is a Pythagorean Triple because 20² + 48² = 400 + 2304 = 2704 = 52².
d) 2, 9, 11:
No, this set of numbers is not a Pythagorean Triple because 2² + 9² = 4 + 81 = 85 ≠ 121 = 11².
e) 39, 80, 89:
Yes, this set of numbers is a Pythagorean Triple because 39² + 80² = 1521 + 6400 = 7921 = 89².