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 cannot represent the sides of a triangle, we can use 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 remaining side. Checking the sets: 1. \( \{6, 10, 15\} \): \( 6 + 10 > 15 \) (no), so this set does not represent a triangle. 2. \( \{10, 25, 33\} \): \( 10 + 25 > 33 \) (no), this set also fails. 3. \( \{14, 18, 30\} \): \( 14 + 18 > 30 \) (no), this set fails. 4. \( \{11, 20, 33\} \): \( 11 + 20 > 33 \) (no), this set fails. Upon reviewing, the triangle inequalities are not satisfied for all sets. Thus, all options can fail to be a triangle, but among them, \( \{6, 10, 15\} \) is clearly the weakest contender as the sides fail explicitly. So, \( \{6, 10, 15\} \) cannot represent the sides of a triangle!