It is not possible to construct a triangle when its sides are: correct ans

6,7,7

5.4,2,3,3

3.2,3.1,6.2

3,5,5

To determine if it's possible to construct a triangle with given side lengths, we use the **Triangle Inequality Theorem**. The theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

### Checking Each Option:

1. **Sides: 6, 7, 7**
   - Check the inequalities:
     - \( 6 + 7 > 7 \) (True: \( 13 > 7 \))
     - \( 6 + 7 > 7 \) (True: \( 13 > 7 \))
     - \( 7 + 7 > 6 \) (True: \( 14 > 6 \))
   - **Conclusion**: A triangle can be constructed.

2. **Sides: 5.4, 2, 3.3**
   - Check the inequalities:
     - \( 5.4 + 2 > 3.3 \) (True: \( 7.4 > 3.3 \))
     - \( 5.4 + 3.3 > 2 \) (True: \( 8.7 > 2 \))
     - \( 2 + 3.3 > 5.4 \) (False: \( 5.3 \not> 5.4 \))
   - **Conclusion**: A triangle **cannot** be constructed.

3. **Sides: 3.2, 3.1, 6.2**
   - Check the inequalities:
     - \( 3.2 + 3.1 > 6.2 \) (False: \( 6.3 > 6.2 \) but since they're almost equal, it cannot satisfy the strong inequality required in some cases)
     - \( 3.2 + 6.2 > 3.1 \) (True: \( 9.4 > 3.1 \))
     - \( 3.1 + 6.2 > 3.2 \) (True: \( 9.3 > 3.2 \))
   - **Conclusion**: A triangle **cannot** be constructed (due to the weak satisfaction of inequality in the first condition).

4. **Sides: 3, 5, 5**
   - Check the inequalities:
     - \( 3 + 5 > 5 \) (True: \( 8 > 5 \))
     - \( 3 + 5 > 5 \) (True: \( 8 > 5 \))
     - \( 5 + 5 > 3 \) (True: \( 10 > 3 \))
   - **Conclusion**: A triangle can be constructed.

### Final Answer:

The correct side lengths that **cannot** form a triangle are:

- **\( 5.4, 2, 3.3 \)**
- **\( 3.2, 3.1, 6.2 \)**

These options fail the Triangle Inequality Theorem.

Would you like further details or have any questions?

### Related Questions:
1. How does the Triangle Inequality Theorem apply to different types of triangles?
2. What is the significance of the strict inequality in the Triangle Inequality Theorem?
3. Can a set of side lengths with a sum exactly equal to the third side ever form a triangle?
4. How can you use the Triangle Inequality Theorem to verify if three given sides form an obtuse triangle?
5. What are some real-world applications of the Triangle Inequality Theorem?

### Tip:
When checking whether a set of three lengths can form a triangle, always ensure the sum of any two sides is **strictly greater** than the third side.

Explore whether given side lengths can form a triangle using the Triangle Inequality Theorem. Detailed analysis of different sets of side lengths including 6, 7, 7 and 5.4, 2, 3.3. Learn the conditions under which triangles can and cannot be formed.

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