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Which set of side lengths does not form a triangle? All lengths are given in inches.(1 point)Responses18, 11, 8 18, 11, 8 9, 17, 11 9, 17, 11 18, 10, 8 18, 10, 8 11, 19, 9

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To determine if a set of 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. \( b + c > a \)

Now we'll check each set of lengths:

  1. 18, 11, 8:

    • \( 18 + 11 = 29 > 8 \) ✔
    • \( 18 + 8 = 26 > 11 \) ✔
    • \( 11 + 8 = 19 > 18 \) ✖
    • This set can form a triangle.

  2. 9, 17, 11:

    • \( 9 + 17 = 26 > 11 \) ✔
    • \( 9 + 11 = 20 > 17 \) ✖
    • \( 17 + 11 = 28 > 9 \) ✔
    • This set can form a triangle.

  3. 18, 10, 8:

    • \( 18 + 10 = 28 > 8 \) ✔
    • \( 18 + 8 = 26 > 10 \) ✔
    • \( 10 + 8 = 18 \) ✖ (not greater, just equal)
    • This set cannot form a triangle.

  4. 11, 19, 9:

    • \( 11 + 19 = 30 > 9 \) ✔
    • \( 11 + 9 = 20 > 19 \) ✖
    • \( 19 + 9 = 28 > 11 \) ✔
    • This set cannot form a triangle.

Based on these evaluations, the sets of lengths 18, 10, 8 and 11, 19, 9 do not form a triangle. However, since one set is asked, the one that fails first is 18, 10, 8.