To solve the problem, we will follow these steps:
### Step 1: Calculate the area of the rectangular grassy plot.
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
Given:
- Length = 112 m
- Breadth = 78 m
Calculating the area:
\[ \text{Area of the plot} = 112 \, \text{m} \times 78 \, \text{m} = 8736 \, \text{m}^2 \]
### Step 2: Calculate the dimensions of the plot excluding the gravel path.
The gravel path is 2.5 m wide on all sides. Therefore, we need to subtract twice the width of the path from both the length and breadth of the plot.
New Length:
\[ \text{New Length} = 112 \, \text{m} - 2 \times 2.5 \, \text{m} = 112 \, \text{m} - 5 \, \text{m} = 107 \, \text{m} \]
New Breadth:
\[ \text{New Breadth} = 78 \, \text{m} - 2 \times 2.5 \, \text{m} = 78 \, \text{m} - 5 \, \text{m} = 73 \, \text{m} \]
### Step 3: Calculate the area of the grassy plot excluding the gravel path.
Using the new dimensions:
\[ \text{Area of the inner plot} = \text{New Length} \times \text{New Breadth} \]
\[ \text{Area of the inner plot} = 107 \, \text{m} \times 73 \, \text{m} = 7811 \, \text{m}^2 \]
### Step 4: Calculate the area of the gravel path.
The area of the path can be found by subtracting the area of the inner plot from the area of the entire plot:
\[ \text{Area of the path} = \text{Area of the plot} - \text{Area of the inner plot} \]
\[ \text{Area of the path} = 8736 \, \text{m}^2 - 7811 \, \text{m}^2 = 925 \, \text{m}^2 \]
### Step 5: Calculate the cost of constructing the gravel path.
The cost is given as Rs. 120 per square meter. Therefore, the total cost can be calculated as:
\[ \text{Cost} = \text{Area of the path} \times \text{Cost per m}^2 \]
\[ \text{Cost} = 925 \, \text{m}^2 \times 120 \, \text{Rs/m}^2 = 111000 \, \text{Rs} \]
### Final Answers:
- Area of the path: 925 m²
- Cost of constructing the path: Rs. 111000
