Question

Which set of side lengths does not form a triangle? All lengths are given in inches.(1 point)Responses18, 10, 818, 10, 818, 11, 818, 11, 89, 17, 119, 17, 1111, 19, 9

Answer 1

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

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

Let's examine each given set of lengths:

1. **(18, 10, 8)**:
- \( 18 + 10 > 8 \) (True)
- \( 18 + 8 > 10 \) (True)
- \( 10 + 8 > 18 \) (False) → **Cannot form a triangle**

2. **(18, 10, 8)** (Repeating):
- As above, it cannot form a triangle.

3. **(18, 11, 8)**:
- \( 18 + 11 > 8 \) (True)
- \( 18 + 8 > 11 \) (True)
- \( 11 + 8 > 18 \) (False) → **Cannot form a triangle**

4. **(9, 17, 11)**:
- \( 9 + 17 > 11 \) (True)
- \( 9 + 11 > 17 \) (False) → **Cannot form a triangle**

5. **(19, 9, 11)**:
- \( 19 + 9 > 11 \) (True)
- \( 19 + 11 > 9 \) (True)
- \( 9 + 11 > 19 \) (False) → **Cannot form a triangle**

From the analysis above, the sets that do not form a triangle are:

1. (18, 10, 8)
2. (18, 11, 8)
3. (9, 17, 11)
4. (19, 9, 11)

**Therefore, there are multiple sets that do not form a triangle. If only one set is to be chosen, any of those above could suffice.**