1. **State the problem:** Determine which sets of side lengths can form a triangle. 2. **Triangle inequality rule:** For any three sides $a$, $b$, and $c$ to form a triangle, the sum of any two sides must be greater than the third side: $$a + b > c, \quad a + c > b, \quad b + c > a$$ 3. **Check each set:** - For sides 6, 7, 14: $$6 + 7 = 13 \not> 14$$ Fails the inequality, so no triangle. - For sides 3, 4, 5: $$3 + 4 = 7 > 5$$ $$3 + 5 = 8 > 4$$ $$4 + 5 = 9 > 3$$ All inequalities hold, so these sides form a triangle. - For sides 15, 15, 36: $$15 + 15 = 30 \not> 36$$ Fails the inequality, so no triangle. - For sides 2, 9, 11: $$2 + 9 = 11 \not> 11$$ Fails the inequality, so no triangle. 4. **Conclusion:** Only the set 3, 4, 5 forms a triangle.