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 9, 17, 11 9, 17, 11 18, 11, 8

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 any three lengths \(a\), \(b\), and \(c\):

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

We will check each set of lengths:

1. **11, 19, 9:**
- \(11 + 19 = 30 > 9\) (True)
- \(11 + 9 = 20 > 19\) (False)
- \(19 + 9 = 28 > 11\) (True)

This set does not form a triangle because the second condition fails.

2. **18, 10, 8:**
- \(18 + 10 = 28 > 8\) (True)
- \(18 + 8 = 26 > 10\) (True)
- \(10 + 8 = 18 > 18\) (False)

This set does not form a triangle because the third condition fails.

3. **9, 17, 11:**
- \(9 + 17 = 26 > 11\) (True)
- \(9 + 11 = 20 > 17\) (True)
- \(17 + 11 = 28 > 9\) (True)

This set does form a triangle.

4. **18, 11, 8:**
- \(18 + 11 = 29 > 8\) (True)
- \(18 + 8 = 26 > 11\) (True)
- \(11 + 8 = 19 > 18\) (True)

This set does form a triangle.

After analyzing all sets, the only set that does not form a triangle is **11, 19, 9**.