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Which of the following sets of three lengths could be the side lengths of a triangle?

A$4$, $7$, $12$
B$3$, $4$, $7$
C$5$, $6$, $9$
D$2$, $8$, $11$
Answer & Solution
Correct answer: C. $5$, $6$, $9$
The triangle inequality requires that the length of each side be **strictly less than** the sum of the other two. - A: $12 > 4 + 7 = 11$. Fails. - B: $7 = 3 + 4$. Fails (must be *strictly* less). - C: $9 < 5 + 6 = 11$, $6 < 5 + 9$, $5 < 6 + 9$ — all three checks pass. ✓ - D: $11 > 2 + 8 = 10$. Fails. Only C works.
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