Which of these IS a Pythagorean triple?ResponsesA 3, 4, 53, 4, 5B 6, 8, 156, 8, 15C 5, 11, 125, 11, 12D 9, 24, 259, 24, 25E 7, 40, 41

The Pythagorean theorem states that in a right 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 can be written as: a² + b² = c².

Let's check each option:

A. 3, 4, 5: 3² + 4² = 9 + 16 = 25, which is equal to 5². So, this is a Pythagorean triple.

B. 6, 8, 15: 6² + 8² = 36 + 64 = 100, which is not equal to 15² (225). So, this is not a Pythagorean triple.

C. 5, 11, 12: 5² + 11² = 25 + 121 = 146, which is not equal to 12² (144). So, this is not a Pythagorean triple.

D. 9, 24, 25: 9² + 24² = 81 + 576 = 657, which is not equal to 25² (625). So, this is not a Pythagorean triple.

E. 7, 40, 41: 7² + 40² = 49 + 1600 = 1649, which is equal to 41². So, this is a Pythagorean triple.

So, the Pythagorean triples among the options given are A (3, 4, 5) and E (7, 40, 41).