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

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.

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 
15² + 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