Which of the following sets of numbers could not represent the three sides of a triangle? Answer Attempt 1 out of 2 \( \{6,10,15\} \) \( \{10,25,33\} \) \( \{14,18,30\} \) \( \{11,20,33\} \)

To determine which set of numbers could not represent the three sides of a triangle, we can use the triangle inequality theorem. This theorem states that for any triangle with sides \(a\), \(b\), and \(c\), the following conditions must hold: 1. \(a + b > c\) 2. \(a + c > b\) 3. \(b + c > a\) We will check each set of numbers against these conditions. ### Set 1: \( \{6, 10, 15\} \) - Check \(6 + 10 > 15\): \(16 > 15\) (True) - Check \(6 + 15 > 10\): \(21 > 10\) (True) - Check \(10 + 15 > 6\): \(25 > 6\) (True) All conditions are satisfied. ### Set 2: \( \{10, 25, 33\} \) - Check \(10 + 25 > 33\): \(35 > 33\) (True) - Check \(10 + 33 > 25\): \(43 > 25\) (True) - Check \(25 + 33 > 10\): \(58 > 10\) (True) All conditions are satisfied. ### Set 3: \( \{14, 18, 30\} \) - Check \(14 + 18 > 30\): \(32 > 30\) (True) - Check \(14 + 30 > 18\): \(44 > 18\) (True) - Check \(18 + 30 > 14\): \(48 > 14\) (True) All conditions are satisfied. ### Set 4: \( \{11, 20, 33\} \) - Check \(11 + 20 > 33\): \(31 > 33\) (False) - Check \(11 + 33 > 20\): \(44 > 20\) (True) - Check \(20 + 33 > 11\): \(53 > 11\) (True) The first condition fails. ### Conclusion The set of numbers that could not represent the three sides of a triangle is \( \{11, 20, 33\} \).