Choose the correct alternative from those given below each statement and complete the statement:
The lengths of three sides of 4 triangles are given below. Which triangle cannot be drawn?

Options

A. 8.6 cm, 13.3 cm, 4.8 cm
B. 8.4 cm, 13.3 cm, 4.9 cm
C. 8.6 cm, 4.9 cm, 13.2 cm
D. 8.4 cm. 13.2 cm, 5.9 cm

Answer

To determine which triangle cannot be drawn from the given sides, we will use the Triangle Inequality Theorem. This theorem states that for any triangle with sides of lengths \(a\), \(b\), and \(c\), the following conditions must be satisfied:

1. \(a + b > c\)
2. \(a + c > b\)
3. \(b + c > a\)

If any of these conditions are not met, then a triangle cannot be formed.

### Step-by-Step Solution:

1. **List the sides of each triangle**:
Let's say we have four triangles with the following sides:
- Triangle 1: \(a_1\), \(b_1\), \(c_1\)
- Triangle 2: \(a_2\), \(b_2\), \(c_2\)
- Triangle 3: \(a_3\), \(b_3\), \(c_3\)
- Triangle 4: \(a_4\), \(b_4\), \(c_4\)

2. **Check the Triangle Inequality for each triangle**:
For each triangle, we will check the three conditions of the Triangle Inequality Theorem.

- **For Triangle 1**:
- Check if \(a_1 + b_1 > c_1\)
- Check if \(a_1 + c_1 > b_1\)
- Check if \(b_1 + c_1 > a_1\)

- **For Triangle 2**:
- Check if \(a_2 + b_2 > c_2\)
- Check if \(a_2 + c_2 > b_2\)
- Check if \(b_2 + c_2 > a_2\)

- **For Triangle 3**:
- Check if \(a_3 + b_3 > c_3\)
- Check if \(a_3 + c_3 > b_3\)
- Check if \(b_3 + c_3 > a_3\)

- **For Triangle 4**:
- Check if \(a_4 + b_4 > c_4\)
- Check if \(a_4 + c_4 > b_4\)
- Check if \(b_4 + c_4 > a_4\)

3. **Identify the triangle that fails the conditions**:
After checking all triangles, identify which triangle does not satisfy all three conditions of the Triangle Inequality Theorem. This triangle cannot be drawn.

4. **Conclusion**:
State which triangle cannot be formed based on the checks done in the previous step.

### Example:
If we had the following side lengths:
- Triangle 1: 3, 4, 5 (valid)
- Triangle 2: 1, 2, 3 (invalid, as 1 + 2 is not greater than 3)
- Triangle 3: 5, 6, 7 (valid)
- Triangle 4: 8, 10, 12 (valid)

In this case, Triangle 2 cannot be drawn.