Can a triangle have three sides whose length are
3 . 4 cm, 4 . 7 cm, 8 cm ?

Answer

To determine if a triangle can be formed with sides of lengths 3.4 cm, 4.7 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.

Let's analyze the given lengths step by step:

1. **Identify the lengths of the sides**:
- Side A = 3.4 cm
- Side B = 4.7 cm
- Side C = 8 cm

2. **Check the first condition**:
- Sum of Side A and Side B should be greater than Side C.
- Calculation:
\[ 3.4 \, \text{cm} + 4.7 \, \text{cm} = 8.1 \, \text{cm} \]
- Compare with Side C:
\[ 8.1 \, \text{cm} > 8 \, \text{cm} \quad \text{(True)} \]

3. **Check the second condition**:
- Sum of Side A and Side C should be greater than Side B.
- Calculation:
\[ 3.4 \, \text{cm} + 8 \, \text{cm} = 11.4 \, \text{cm} \]
- Compare with Side B:
\[ 11.4 \, \text{cm} > 4.7 \, \text{cm} \quad \text{(True)} \]

4. **Check the third condition**:
- Sum of Side B and Side C should be greater than Side A.
- Calculation:
\[ 4.7 \, \text{cm} + 8 \, \text{cm} = 12.7 \, \text{cm} \]
- Compare with Side A:
\[ 12.7 \, \text{cm} > 3.4 \, \text{cm} \quad \text{(True)} \]

Since all three conditions of the triangle inequality theorem are satisfied, we conclude that:

**Final Answer**: Yes, a triangle can be formed with sides measuring 3.4 cm, 4.7 cm, and 8 cm.