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

Question

Responses

9, 17, 11
9, 17, 11

11, 19, 9
11, 19, 9

18, 10, 8
18, 10, 8

18, 11, 8

Answer 1

To determine which set of side lengths does not form a triangle, we can use the triangle inequality theorem. According to this theorem, for any three sides (a, b, and c), the following conditions must be satisfied:

1. a + b > c
2. a + c > b
3. b + c > a

Let's evaluate each set of side lengths:

1. 9, 17, 11:

   • 9 + 17 > 11 (26 > 11) ✅
   • 9 + 11 > 17 (20 > 17) ✅
   • 17 + 11 > 9 (28 > 9) ✅
   • This set forms a triangle.

2. 11, 19, 9:

   • 11 + 19 > 9 (30 > 9) ✅
   • 11 + 9 > 19 (20 > 19) ✅
   • 19 + 9 > 11 (28 > 11) ✅
   • This set forms a triangle.

3. 18, 10, 8:

   • 18 + 10 > 8 (28 > 8) ✅
   • 18 + 8 > 10 (26 > 10) ✅
   • 10 + 8 > 18 (18 > 18) ❌
   • This set does not form a triangle.

4. 18, 11, 8:

   • 18 + 11 > 8 (29 > 8) ✅
   • 18 + 8 > 11 (26 > 11) ✅
   • 11 + 8 > 18 (19 > 18) ✅
   • This set forms a triangle.

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