Geometry

Question Analysis:  
This question tests the Triangle Inequality Theorem, which states that the sum of any two sides of a triangle must be greater than the third side.
The main focus is identifying which set of side lengths violates this rule.  

Key Concept Explanation:  
- For three lengths to form a triangle, the following must be true:  
 - a + b > c  
 - a + c > b  
 - b + c > a  
- If any one of these inequalities fails, the sides cannot form a triangle.  

Step-by-Step Solution:  
1. Check Option A (5, 6, 7):  
  - 5 + 6 > 7 → 11 > 7 ✔️  
  - 5 + 7 > 6 → 12 > 6 ✔️  
  - 6 + 7 > 5 → 13 > 5 ✔️  
  → Valid triangle.  
2. Check Option B (3, 4, 8):  
  - 3 + 4 > 8 → 7 < 8 ❌ (Fails)  
  → Cannot form a triangle.  
3. Check Options C & D for completeness:  
  - C (9, 12, 15): All sums valid (e.g., 9 + 12 > 15).  
  - D (10, 1...