Answer: The set of numbers that could represent the lengths of the sides of a right triangle is 7, 24, 25.
Step-by-step explanation: In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. This is called the Pythagorean theorem. So, we can check each set of numbers by seeing if they satisfy the Pythagorean theorem. Let's check: For 7, 24, 25: 7² + 24² = 49 + 576 = 625 25² = 625 As both sides are equal, the set of numbers 7, 24, 25 can represent the lengths of the sides of a right triangle. For 6, 9, 11: 6² + 9² = 36 + 81 = 117 11² = 121 As both sides are not equal, the set of numbers 6, 9, 11 cannot represent the lengths of the sides of a right triangle. For 10, 15, 20: 10² + 15² = 100 + 225 = 325 20² = 400 As both sides are not equal, the set of numbers 10, 15, 20 cannot represent the lengths of the sides of a right triangle. For 9, 12, 16: 9² + 12² = 81 + 144 = 225 16² = 256 As both sides are not equal, the set of numbers 9, 12, 16 cannot represent the lengths of the sides of a right triangle. Therefore, the only set of numbers that could represent the lengths of the sides of a right triangle is 7, 24, 25.