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

Question

Responses

11, 19, 9
11, 19, 9

9, 17, 11
9, 17, 11

18, 11, 8
18, 11, 8

18, 10, 8

Answer 1

To determine if a set of side lengths can form a triangle, we use the triangle inequality theorem. This theorem states that for any three lengths \(a\), \(b\), and \(c\), the following must be true:

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

Let's check each set of side 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. 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.

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. 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.

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