Final answer:
The triangle with side lengths 9, 12, and 15 is a right triangle. This is determined by using the Pythagorean Theorem, which shows that the square of the longest side is equal to the sum of the squares of the other two sides.
Step-by-step explanation:
In mathematics, we can classify triangles based on their side lengths using the Pythagorean Theorem. This theorem states that in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. If we test the side lengths of our triangle, 9, 12, and 15, we find that 92 + 122 = 81 + 144 = 225, and 152 also equals 225. Since these sums are equal, we are dealing with a right triangle.
Learn more about Triangle Classification