Question

Question
Which set of side lengths does not form a triangle? All lengths are given in inches.(1 point)
Responses

11, 19, 9
11, 19, 9

18, 10, 8
18, 10, 8

18, 11, 8
18, 11, 8

9, 17, 11
9, 17, 11
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Answer 1

To determine which set of side lengths does not form a triangle, we can use the triangle inequality theorem. This theorem states that for three sides of lengths \( a \), \( b \), and \( c \) to form a triangle, the following conditions must hold true:

1. \( a + b > c \)
2. \( a + c > b \)
3. \( b + c > a \)

We'll check each of the provided sets of lengths:

1. **11, 19, 9**
- \( 11 + 19 > 9 \) → 30 > 9 (True)
- \( 11 + 9 > 19 \) → 20 > 19 (True)
- \( 19 + 9 > 11 \) → 28 > 11 (True)
- This set can form a triangle.

2. **18, 10, 8**
- \( 18 + 10 > 8 \) → 28 > 8 (True)
- \( 18 + 8 > 10 \) → 26 > 10 (True)
- \( 10 + 8 > 18 \) → 18 > 18 (False)
- This set cannot form a triangle.

3. **18, 11, 8**
- \( 18 + 11 > 8 \) → 29 > 8 (True)
- \( 18 + 8 > 11 \) → 26 > 11 (True)
- \( 11 + 8 > 18 \) → 19 > 18 (True)
- This set can form a triangle.

4. **9, 17, 11**
- \( 9 + 17 > 11 \) → 26 > 11 (True)
- \( 9 + 11 > 17 \) → 20 > 17 (True)
- \( 17 + 11 > 9 \) → 28 > 9 (True)
- This set can form a triangle.

The only set of lengths that does not satisfy the triangle inequality conditions is **18, 10, 8**.