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Let's break down the problem:

### Given:
- The garden is **100 m** long and **50 m** wide.
- There is a road of **3 m** wide around the garden.
- The cost of paving the road is **Rs. 250 per square meter**.

### To Find:
The total cost of paving the road.

### Approach:

1. **Area of the garden (without the road):**
   - Length = 100 m
   - Width = 50 m
   \[
   \text{Area of garden} = \text{Length} \times \text{Width} = 100 \times 50 = 5000 \, \text{m}^2
   \]

2. **Area of the garden including the road:**
   - Since the road is around the garden, the total dimensions increase by 3 m on each side.
   - New Length = \(100 + 2 \times 3 = 106 \, \text{m}\)
   - New Width = \(50 + 2 \times 3 = 56 \, \text{m}\)
   \[
   \text{Area of garden with road} = \text{New Length} \times \text{New Width} = 106 \times 56 = 5936 \, \text{m}^2
   \]

3. **Area of the road:**
   The area of the road is the difference between the area of the garden with the road and the area of the garden without the road:
   \[
   \text{Area of road} = \text{Area with road} - \text{Area of garden} = 5936 - 5000 = 936 \, \text{m}^2
   \]

4. **Cost of paving the road:**
   The cost is given as Rs. 250 per square meter.
   \[
   \text{Cost} = 936 \times 250 = 234000 \, \text{Rs}
   \]

### Answer:
The cost of paving the road is **Rs. 234,000**.

Would you like more details, or do you have any further questions?

Here are 5 related questions for practice:
1. If the cost per square meter increased to Rs. 300, what would be the new total cost?
2. How much area would the road cover if the garden was square, with a side length of 60 meters?
3. What would be the cost if the road was only 2 meters wide instead of 3 meters?
4. How would the area of the road change if the garden was 150 m long and 70 m wide?
5. How much would it cost to pave a circular road with a radius of 5 meters around a circular garden?

**Tip**: When calculating areas, always account for the increase in dimensions on both sides when something surrounds a given area.

A garden 100 m long and 50 m wide has a road 3 m wide all around the garden. Find the cost of paving the road at the rate of Rs. 250 per m².

Learn how to calculate the cost of paving a road around a garden. This example covers geometry concepts, including area calculation and cost determination based on the area of the road. Suitable for students in Grades 6-8.

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