Which triplets of numbers can form a Pythagorean triple? Select one of the options below as your answer:
A. 5, 7, 9
B. 6, 9, 12
C. 10, 12, 15
D. none of the above
To determine if a set of numbers forms a Pythagorean triple, you need to check if the sum of the squares of two of the numbers is equal to the square of the third number.
Let's go through each option:
A. 5, 7, 9
To check if this forms a Pythagorean triple, we need to find if 5^2 + 7^2 = 9^2. Calculating, we get 25 + 49 = 81, which is true. So, option A can form a Pythagorean triple.
B. 6, 9, 12
To check, we need to find if 6^2 + 9^2 = 12^2. Calculating, we get 36 + 81 = 144, which is true. Therefore, option B can form a Pythagorean triple.
C. 10, 12, 15
Again, we need to check if 10^2 + 12^2 = 15^2. Calculating, we get 100 + 144 = 225, which is true. So, option C can form a Pythagorean triple.
D. none of the above
Since the previous options are all capable of forming Pythagorean triples, option D is incorrect.
Therefore, the correct answer is:
A. 5, 7, 9
B. 6, 9, 12
C. 10, 12, 15