To determine whether a set of side lengths can form a triangle, we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides must be greater than the length of the third side.
Let's analyze the given sets of side lengths:
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18, 11, 8
- 18 + 11 > 8 (29 > 8) ✔
- 18 + 8 > 11 (26 > 11) ✔
- 11 + 8 > 18 (19 > 18) ✔
- This set can form a triangle.
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18, 11, 89
- 18 + 11 > 89 (29 > 89) ✖
- This set cannot form a triangle.
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17, 11
- Lacks a third side to make a triangle, but since only two sides are provided, it cannot form a triangle.
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17, 11, 18
- 17 + 11 > 18 (28 > 18) ✔
- 17 + 18 > 11 (35 > 11) ✔
- 11 + 18 > 17 (29 > 17) ✔
- This set can form a triangle.
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10, 8
- Also lacks a third side for a triangle and cannot form a triangle as is.
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10, 8, 11
- 10 + 8 > 11 (18 > 11) ✔
- 10 + 11 > 8 (21 > 8) ✔
- 8 + 11 > 10 (19 > 10) ✔
- This set can form a triangle.
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19, 9
- Lacks a third side as well for a triangle and cannot form a triangle as is.
Based on the analysis, the set of lengths 18, 11, 89 does not form a triangle because it violates the triangle inequality theorem.
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