Which of the following sets of numbers could not represent the three sides of a triangle? Answer Attempt s out of 2 \( \{13,17,27\} \) \( \begin{array}{lll}\{8,16,22\} & \{12,19,30\} & \text { Submit Answer } \\ \{12,26,38\} & \end{array} \)

To determine if a set of numbers can represent the sides of a triangle, you can apply the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides must be greater than the length of the third side. For the set \( \{12,19,30\} \), let's check: 1. \(12 + 19 = 31 > 30\) (valid) 2. \(12 + 30 = 42 > 19\) (valid) 3. \(19 + 30 = 49 > 12\) (valid) All conditions are met, so this set can represent a triangle. Now, if we check the set \( \{8,16,22\} \): 1. \(8 + 16 = 24 > 22\) (valid) 2. \(8 + 22 = 30 > 16\) (valid) 3. \(16 + 22 = 38 > 8\) (valid) This set also meets the requirements. Finally, checking \( \{12,26,38\} \): 1. \(12 + 26 = 38\) (not greater than) 2. \(12 + 38 = 50 > 26\) (valid) 3. \(26 + 38 = 64 > 12\) (valid) Since the first condition fails, this set cannot represent a triangle. Thus, your answer is \( \{12, 19, 30\} \).