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

1 answer

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.