Which set of numbers is not considered a Pythagorean triple?

To determine which set of numbers is not considered a Pythagorean triple, we need to evaluate each set based on the Pythagorean theorem, which states that for a set of three numbers (a), (b), and (c) (where (c) is the largest number), they form a Pythagorean triple if (a^2 + b^2 = c^2).

For Set D: the numbers are 8, 15, and 16. Here, 16 is the largest number, so we should check if (8^2 + 15^2) equals (16^2).

Calculating each square:

• (8^2 = 64)

• (15^2 = 225)

• (16^2 = 256)

Now add the squares of 8 and 15:

(64 + 225 = 289)

We see that (289) does not equal (256) (which is (16^2)). Therefore, the numbers 8, 15, and 16 do not satisfy the Pythagorean theorem.

In contrast, the other sets do satisfy the relationship defined by