Question Which of the following sets of numbers could not represent the three sides of a triangle? Answer \( \begin{array}{l}\{11,19,32\} \\ \{8,18,24\} \\ \{11,23,31\} \\ \{7,22,27\}\end{array} \) \( \begin{array}{l}\text { Show Examples } \\ \text { You have up to } 33 \text { questions left to raise your score. }\end{array} \)

To determine which set of numbers **cannot** represent the sides of a triangle, we can use the **Triangle Inequality Theorem**. This theorem states that for any three sides to form a valid triangle, the sum of any two sides must be **greater** than the third side. Let's examine each set: 1. **\{11, 19, 32\}** - **11 + 19 = 30** - **30** is **not greater** than **32** Since the sum of the two smaller sides (11 and 19) is **less than** the largest side (32), this set **cannot** form a valid triangle. 2. **\{8, 18, 24\}** - **8 + 18 = 26 > 24** - **8 + 24 = 32 > 18** - **18 + 24 = 42 > 8** All combinations satisfy the Triangle Inequality Theorem. This set **can** form a valid triangle. 3. **\{11, 23, 31\}** - **11 + 23 = 34 > 31** - **11 + 31 = 42 > 23** - **23 + 31 = 54 > 11** All combinations satisfy the Triangle Inequality Theorem. This set **can** form a valid triangle. 4. **\{7, 22, 27\}** - **7 + 22 = 29 > 27** - **7 + 27 = 34 > 22** - **22 + 27 = 49 > 7** All combinations satisfy the Triangle Inequality Theorem. This set **can** form a valid triangle. **Conclusion:** The set **\{11, 19, 32\}** **cannot** represent the sides of a valid triangle because it fails to satisfy the Triangle Inequality Theorem.