Which type of triangle will obtained from sides 2 cm, 3 cm and 6 cm ?

Options

A. Acute angles triangle
B. Scalene triangle
C. Both 'a' and 'b'
D. None of the above

Answer

To determine the type of triangle that can be formed with sides measuring 2 cm, 3 cm, and 6 cm, we need to use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

### Step-by-Step Solution:

1. **Identify the sides of the triangle**:
Let the sides of the triangle be:
- \( A = 2 \, \text{cm} \)
- \( B = 3 \, \text{cm} \)
- \( C = 6 \, \text{cm} \)

2. **Apply the triangle inequality theorem**:
We need to check the following inequalities:
- \( A + B > C \)
- \( A + C > B \)
- \( B + C > A \)

3. **Check the first inequality**:
- Calculate \( A + B \):
\[ A + B = 2 + 3 = 5 \]
- Compare with \( C \):
\[ 5 > 6 \quad \text{(False)} \]

4. **Check the second inequality**:
- Calculate \( A + C \):
\[ A + C = 2 + 6 = 8 \]
- Compare with \( B \):
\[ 8 > 3 \quad \text{(True)} \]

5. **Check the third inequality**:
- Calculate \( B + C \):
\[ B + C = 3 + 6 = 9 \]
- Compare with \( A \):
\[ 9 > 2 \quad \text{(True)} \]

6. **Conclusion**:
Since the first inequality \( A + B > C \) is false, it indicates that a triangle cannot be formed with the given sides of 2 cm, 3 cm, and 6 cm. Therefore, the answer is that no triangle can be formed with these sides.

### Final Answer:
No triangle can be formed with sides 2 cm, 3 cm, and 6 cm.

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