To determine whether a set of side lengths can form a triangle, we can use the triangle inequality theorem, which states that for any triangle with sides of lengths \( a \), \( b \), and \( c \):
- \( a + b > c \)
- \( a + c > b \)
- \( b + c > a \)
We will apply this theorem to each set of lengths provided.
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For the set (9, 17, 11):
- \( 9 + 11 > 17 \) → \( 20 > 17 \) (True)
- \( 9 + 17 > 11 \) → \( 26 > 11 \) (True)
- \( 11 + 17 > 9 \) → \( 28 > 9 \) (True)
- This set can form a triangle.
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For the set (11, 19, 9):
- \( 11 + 9 > 19 \) → \( 20 > 19 \) (True)
- \( 11 + 19 > 9 \) → \( 30 > 9 \) (True)
- \( 19 + 9 > 11 \) → \( 28 > 11 \) (True)
- This set can form a triangle.
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For the set (18, 10, 8):
- \( 18 + 10 > 8 \) → \( 28 > 8 \) (True)
- \( 18 + 8 > 10 \) → \( 26 > 10 \) (True)
- \( 10 + 8 > 18 \) → \( 18 > 18 \) (False)
- This set cannot form a triangle.
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For the set (18, 11, 8):
- \( 18 + 11 > 8 \) → \( 29 > 8 \) (True)
- \( 18 + 8 > 11 \) → \( 26 > 11 \) (True)
- \( 11 + 8 > 18 \) → \( 19 > 18 \) (True)
- This set can form a triangle.
Based on the analysis, the sets of side lengths that can form a triangle are:
- (9, 17, 11)
- (11, 19, 9)
- (18, 11, 8)
So the correct responses are (9, 17, 11), (11, 19, 9), and (18, 11, 8).