Can a triangle have three sides whose length are
2 . 5 cm, 4 . 5 cm , 8 cm ?

Answer

To determine if a triangle can be formed with sides of lengths 2.5 cm, 4.5 cm, and 8 cm, we need to apply the triangle inequality theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

### Step-by-Step Solution:

1. **Identify the sides of the triangle**:
- Let the sides be \( a = 2.5 \, \text{cm} \), \( b = 4.5 \, \text{cm} \), and \( c = 8 \, \text{cm} \).

2. **Check the first condition**:
- Check if \( a + b > c \):
\[ 2.5 + 4.5 = 7 \, \text{cm} \]
- Since \( 7 \, \text{cm} < 8 \, \text{cm} \), this condition is not satisfied.

3. **Check the second condition**:
- Check if \( a + c > b \):
\[ 2.5 + 8 = 10.5 \, \text{cm} \]
- Since \( 10.5 \, \text{cm} > 4.5 \, \text{cm} \), this condition is satisfied.

4. **Check the third condition**:
- Check if \( b + c > a \):
\[ 4.5 + 8 = 12.5 \, \text{cm} \]
- Since \( 12.5 \, \text{cm} > 2.5 \, \text{cm} \), this condition is satisfied.

5. **Conclusion**:
- Since the first condition \( (a + b > c) \) is not satisfied, we conclude that a triangle cannot be formed with sides of lengths 2.5 cm, 4.5 cm, and 8 cm.

### Summary:
No, a triangle cannot be formed with sides of lengths 2.5 cm, 4.5 cm, and 8 cm because the sum of the lengths of the two shorter sides (2.5 cm and 4.5 cm) is not greater than the length of the longest side (8 cm).