Final answer:
A right triangle is a triangle that has one angle measuring 90 degrees. In a right triangle, the square of the length of one side plus the square of the length of another side is equal to the square of the length of the hypotenuse. The correct answer is option 3: 15, 16, 17.
Step-by-step explanation:
A right triangle is a triangle that has one angle measuring 90 degrees. In a right triangle, the square of the length of one side (called the adjacent side) plus the square of the length of another side (called the opposite side) is equal to the square of the length of the hypotenuse.
Let's check each list of side lengths to see if it represents a right triangle:
3, 6, 9: This does not represent a right triangle because 3^2 + 6^2 = 45 which is not equal to 9^2.
5, 12, 14: This does not represent a right triangle because 5^2 + 12^2 = 169 which is not equal to 14^2.
15, 16, 17: This represents a right triangle because 15^2 + 16^2 = 225 + 256 = 481 which is equal to 17^2.
7, 24, 25: This represents a right triangle because 7^2 + 24^2 = 49 + 576 = 625 which is equal to 25^2.
So, the correct answer is option 3: 15, 16, 17.