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The question in the image asks if you can form a triangle using specific lengths for the sides. To solve this, we apply the **Triangle Inequality Theorem**, which states that for any three sides to form a triangle, the sum of the lengths of any two sides must always be greater than the length of the remaining side.

I'll go through the set of side lengths and check which of them can form a triangle.

1. **5, 7, 9**:
   - 5 + 7 > 9 (True)
   - 5 + 9 > 7 (True)
   - 7 + 9 > 5 (True)
   - **Result**: Can form a triangle.

2. **3, 4, 1**:
   - 3 + 4 > 1 (True)
   - 3 + 1 > 4 (False)
   - 4 + 1 > 3 (True)
   - **Result**: Cannot form a triangle.

3. **3, 3, 4**:
   - 3 + 3 > 4 (True)
   - 3 + 4 > 3 (True)
   - 3 + 4 > 3 (True)
   - **Result**: Can form a triangle.

4. **7, 7, 7**:
   - 7 + 7 > 7 (True)
   - **Result**: Can form a triangle (it's an equilateral triangle).

5. **7, 7, 14**:
   - 7 + 7 = 14 (False)
   - **Result**: Cannot form a triangle (sum must be greater than 14, not equal).

6. **7, 7, 0.01**:
   - 7 + 7 > 0.01 (True)
   - 7 + 0.01 > 7 (False)
   - **Result**: Cannot form a triangle.

7. **12, 2.2, 14.3**:
   - 12 + 2.2 > 14.3 (True)
   - 12 + 14.3 > 2.2 (True)
   - 14.3 + 2.2 > 12 (True)
   - **Result**: Can form a triangle.

8. **5.2, 5.5, 10.1**:
   - 5.2 + 5.5 > 10.1 (True)
   - 5.2 + 10.1 > 5.5 (True)
   - 5.5 + 10.1 > 5.2 (True)
   - **Result**: Can form a triangle.

### Summary:
- Triangles can be formed with the following side lengths: **5, 7, 9**, **3, 3, 4**, **7, 7, 7**, **12, 2.2, 14.3**, and **5.2, 5.5, 10.1**.
- Triangles **cannot** be formed with the following side lengths: **3, 4, 1**, **7, 7, 14**, and **7, 7, 0.01**.

Do you need more details or have any questions?

Here are 5 relative questions:
1. What is the Triangle Inequality Theorem?
2. Why can't a triangle be formed when the sum of two sides equals the third side?
3. Can a triangle be formed with side lengths that are decimals?
4. What are the different types of triangles based on their side lengths?
5. How can the Triangle Inequality Theorem be applied in 3D geometry?

**Tip**: When checking if sides can form a triangle, always ensure that the sum of any two sides is strictly greater than the third side.

Can you draw a triangle using these lengths for the sides: {5, 7, 9}, {3, 4, 1}, {3, 3, 4}, {7, 7, 7}, {7, 7, 14}, {7, 7, 0.01}, {12, 2.2, 14.3}, {5.2, 5.5, 10.1}?

Explore whether a triangle can be formed with the given side lengths using the Triangle Inequality Theorem. We check sets like {5, 7, 9}, {3, 4, 1}, and more. Suitable for Grades 6-8.

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