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Which set of side lengths will form a triangle? All lengths are given in meters.(1 point)

Responses

26, 12, 12
26, 12, 12

50, 60, 26
50, 60, 26

50, 30, 80
50, 30, 80

60, 26, 33

1 answer

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

We will evaluate each set of side lengths against these conditions.

  1. For 26, 12, 12:

    • \( 26 + 12 > 12 \) (True)
    • \( 26 + 12 > 12 \) (True)
    • \( 12 + 12 > 26 \) (False)

    This set does not form a triangle.

  2. For 50, 60, 26:

    • \( 50 + 60 > 26 \) (True)
    • \( 50 + 26 > 60 \) (True)
    • \( 60 + 26 > 50 \) (True)

    This set forms a triangle.

  3. For 50, 30, 80:

    • \( 50 + 30 > 80 \) (False)

    This set does not form a triangle.

  4. For 60, 26, 33:

    • \( 60 + 26 > 33 \) (True)
    • \( 60 + 33 > 26 \) (True)
    • \( 26 + 33 > 60 \) (False)

    This set does not form a triangle.

Conclusion: The only set of side lengths that will form a triangle is 50, 60, 26.