If the numbers 3, 4, 5 form a Pythagorean triple, is the statement True or False?

If the numbers 3, 4, 5 form a Pythagorean triple, is the statement True or False?

• A. False
• B. True
• C. Not a Pythagorean triple
• D. Yes, it's a primitive triple

Answer: (B)

To test whether a set of three positive integers forms a Pythagorean triple, use the Pythagorean relation a^2 + b^2 = c^2 with the largest number as the hypotenuse. Here the largest is 5, so check 3^2 + 4^2 = 9 + 16 = 25, and 5^2 = 25. They match, so these numbers do form a Pythagorean triple, which makes the statement true. It's also a primitive triple since 3, 4, and 5 have no common divisor greater than 1, meaning they are not a multiple of any smaller triple. Therefore, the statement is true, and it is also primitive.

To test whether a set of three positive integers forms a Pythagorean triple, use the Pythagorean relation a^2 + b^2 = c^2 with the largest number as the hypotenuse. Here the largest is 5, so check 3^2 + 4^2 = 9 + 16 = 25, and 5^2 = 25. They match, so these numbers do form a Pythagorean triple, which makes the statement true. It's also a primitive triple since 3, 4, and 5 have no common divisor greater than 1, meaning they are not a multiple of any smaller triple. Therefore, the statement is true, and it is also primitive.