Which of the following sets of numbers could not represent the three sides of a triangle? Answer $$ \{5,9,13\} $$ $$ \{9,21,29\} $$ $$ \{10,20,31\} $$ $$ \{13,27,39\} $$ Submit Answer

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To determine which set of numbers **cannot** represent the sides of a triangle, we use the **triangle inequality theorem**. This theorem states that for any three sides $$ a $$, $$ b $$, and $$ c $$ of a triangle:

1. $$ a + b > c $$
2. $$ a + c > b $$
3. $$ b + c > a $$

Let's evaluate each set:

1. **$$\{5, 9, 13\}$$**
   - $$5 + 9 = 14 > 13$$ ✓
   - $$5 + 13 = 18 > 9$$ ✓
   - $$9 + 13 = 22 > 5$$ ✓
   
   **Valid triangle**

2. **$$\{9, 21, 29\}$$**
   - $$9 + 21 = 30 > 29$$ ✓
   - $$9 + 29 = 38 > 21$$ ✓
   - $$21 + 29 = 50 > 9$$ ✓
   
   **Valid triangle**

3. **$$\{10, 20, 31\}$$**
   - $$10 + 20 = 30 
leq 31$$ ✗
   
   **Invalid triangle**

4. **$$\{13, 27, 39\}$$**
   - $$13 + 27 = 40 > 39$$ ✓
   - $$13 + 39 = 52 > 27$$ ✓
   - $$27 + 39 = 66 > 13$$ ✓
   
   **Valid triangle**

**Conclusion:** The set $$\{10, 20, 31\}$$ **cannot** represent the sides of a triangle.

**Answer:** $$ \{10,20,31\} $$
The set $$\{10, 20, 31\}$$ cannot represent the sides of a triangle.

Which of the following sets of numbers could not represent the three sides of a triangle? Answer \( \{5,9,13\} \) \( \{9,21,29\} \) \( \{10,20,31\} \) \( \{13,27,39\} \) Submit Answer

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