To determine if a set of side lengths can form a triangle, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's evaluate each set of side lengths:
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26, 12, 12:
- \( 26 < 12 + 12 \) (26 < 24, false)
- This set cannot form a triangle.
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50, 30, 80:
- \( 80 < 50 + 30 \) (80 < 80, false)
- This set cannot form a triangle.
-
50, 60, 26:
- \( 50 + 26 > 60 \) (76 > 60, true)
- \( 50 + 60 > 26 \) (110 > 26, true)
- \( 60 + 26 > 50 \) (86 > 50, true)
- This set can form a triangle.
-
60, 26, 33:
- \( 60 + 26 > 33 \) (86 > 33, true)
- \( 60 + 33 > 26 \) (93 > 26, true)
- \( 26 + 33 > 60 \) (59 > 60, false)
- This set cannot form a triangle.
Based on the triangle inequality theorem, the only set of side lengths that can form a triangle is 50, 60, 26.