Which of the following is not a pythagorean triple? A. 15, 36, 39 B. 24, 45, 51 C. 21, 72, 76 D. 18, 24, 30

The answer is C. 21, 72, 76

The Pythagorean theorem states that the square of the hypotenuse (c) is equal to the sum of the squares of two other sides (a, b):

a² + b² = c²

So, let's start with checking out the choices:

A. 15, 36, 39

a = 15

b = 36

c = 39

a² + b² = c²

15 ² + 36² = 39²

225 + 1296 = 1521

1521 = 1521

B. 24, 45, 51

a = 24

b = 45

c = 51

a² + b² = c²

24² + 45² = 51²

576 + 2025 = 2601

2601 = 2601

C. 21, 72, 76

a = 21

b = 72

c = 76

a² + b² = c²

21² + 72² = 76²

441 + 5184 = 5776

5625 ≠ 5776

Pythagorean triple: a² + b² = c²

A) 15² + 36² = 39² ⇒ 225 + 1296 = 1521 ⇒ 1521 = 1521

B) 24² + 45² = 51² ⇒ 576 + 2025 = 2601 ⇒ 2601 = 2601

C) 21² + 72² = 76² ⇒ 441 + 5184 = 5776 ⇒ 5625 ≠ 5776

D) 18² + 24² = 30² ⇒ 324 + 576 = 900 ⇒ 900 = 900

C) 21, 72, 76 is not a pythagorean triple.