Question

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

18, 11, 8
18, 11, 8

18, 10, 8
18, 10, 8

11, 19, 9
11, 19, 9

9, 17, 11

Answer 1

To determine whether a set of side lengths can form a triangle, we can use the triangle inequality theorem. This theorem states that for any triangle with sides of lengths \(a\), \(b\), and \(c\):

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

Let's apply this to each set of side lengths:

1. **18, 11, 8**
- \(18 + 11 = 29 > 8\) (True)
- \(18 + 8 = 26 > 11\) (True)
- \(11 + 8 = 19 > 18\) (True)
- This set can form a triangle.

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

3. **11, 19, 9**
- \(11 + 19 = 30 > 9\) (True)
- \(11 + 9 = 20 > 19\) (True)
- \(19 + 9 = 28 > 11\) (True)
- This set can form a triangle.

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

Thus, the set of side lengths that **does not** form a triangle is:

**18, 10, 8**.