Problem

Which of the following are possible side lengths for a triangle?
A. $4,16,11$
B. $2,10,6$
C. $6,8,9$

Answer

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Answer

Final Answer: Only the side lengths \(\boxed{(6, 8, 9)}\) can form a triangle.

Steps

Step 1 ：The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than or equal to the length of the remaining side. We can use this theorem to determine which of the given sets of side lengths could form a triangle.

Step 2 ：Given options are \((4, 16, 11), (2, 10, 6), (6, 8, 9)\)

Step 3 ：Checking each option, we find that only the side lengths \((6, 8, 9)\) can form a triangle.

Step 4 ：Final Answer: Only the side lengths \(\boxed{(6, 8, 9)}\) can form a triangle.

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