If 22.5 metres of a uniform iron rod weighs 85.5 kg.What will be the length of 22.8 kg of the same rod?

Answer

To solve the problem, we will use the unitary method. We know the weight of the iron rod and its corresponding length, and we need to find the length of a different weight of the same rod.

### Step-by-Step Solution:

1. **Identify the given information:**
- Length of the rod for 85.5 kg = 22.5 m
- Weight we want to find the length for = 22.8 kg

2. **Find the length of 1 kg of the rod:**
- To find the length of 1 kg of the rod, we can use the formula:
\[ \text{Length of 1 kg} = \frac{\text{Length of rod}}{\text{Weight of rod}} = \frac{22.5 \text{ m}}{85.5 \text{ kg}} \]

3. **Calculate the length of 1 kg:**
- Performing the calculation:
\[ \text{Length of 1 kg} = \frac{22.5}{85.5} \approx 0.2632 \text{ m} \]

4. **Find the length of 22.8 kg of the rod:**
- Now, we can find the length of 22.8 kg of the rod using:
\[ \text{Length of 22.8 kg} = \text{Length of 1 kg} \times 22.8 \]
- Substituting the value we found:
\[ \text{Length of 22.8 kg} = 0.2632 \text{ m} \times 22.8 \]

5. **Calculate the length of 22.8 kg:**
- Performing the multiplication:
\[ \text{Length of 22.8 kg} \approx 6.0 \text{ m} \]

### Final Answer:
The length of 22.8 kg of the same iron rod is approximately **6.0 meters**.