Question

Which set of side lengths does not form a triangle? All lengths are given in inches. (1 point)
О 11, 19,9
О 18, 11,8
О 18, 10,8
0 9,17,11

Answer 1

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

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

Let's evaluate each set of side lengths:

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

2. **18, 11, 8:**
- \(18 + 11 = 29 > 8\) (True)
- \(18 + 8 = 26 > 11\) (True)
- \(11 + 8 = 19 > 18\) (True)
- **Forms a triangle**

3. **18, 10, 8:**
- \(18 + 10 = 28 > 8\) (True)
- \(18 + 8 = 26 > 10\) (True)
- \(10 + 8 = 18\) (Not greater than 18, so this fails)
- **Does not form a triangle**

4. **9, 17, 11:**
- \(9 + 11 = 20 > 17\) (True)
- \(9 + 17 = 26 > 11\) (True)
- \(17 + 11 = 28 > 9\) (True)
- **Forms a triangle**

The set of side lengths that does not form a triangle is **18, 10, 8**.