A rectangular grassy plot is 75 m long and 60 m broad. It has a path of width 2 m all around it on the inside. Find the area of the path and the cost of constructing it atRs.  125 per `m^(2)`

Answer

To solve the problem step by step, let's break it down into manageable parts.

### Step 1: Calculate the area of the rectangular grassy plot.
The formula for the area of a rectangle is:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]

Given:
- Length = 75 m
- Breadth = 60 m

Calculating the area:
\[ \text{Area of the plot} = 75 \, \text{m} \times 60 \, \text{m} = 4500 \, \text{m}^2 \]

### Step 2: Determine the dimensions of the inner rectangle (the grassy area without the path).
Since the path is 2 m wide on all sides, we need to subtract 4 m from both the length and the breadth (2 m from each side).

Calculating the new dimensions:
- New Length = \( 75 \, \text{m} - 4 \, \text{m} = 71 \, \text{m} \)
- New Breadth = \( 60 \, \text{m} - 4 \, \text{m} = 56 \, \text{m} \)

### Step 3: Calculate the area of the inner rectangle (the grassy area).
Using the formula for the area of a rectangle again:
\[ \text{Area of the inner rectangle} = \text{New Length} \times \text{New Breadth} \]

Calculating the area:
\[ \text{Area of the inner rectangle} = 71 \, \text{m} \times 56 \, \text{m} = 3976 \, \text{m}^2 \]

### Step 4: Calculate the area of the path.
To find the area of the path, subtract the area of the inner rectangle from the area of the outer rectangle (the grassy plot).

Calculating the area of the path:
\[ \text{Area of the path} = \text{Area of the plot} - \text{Area of the inner rectangle} \]
\[ \text{Area of the path} = 4500 \, \text{m}^2 - 3976 \, \text{m}^2 = 524 \, \text{m}^2 \]

### Step 5: Calculate the cost of constructing the path.
Given the cost of constructing the path is Rs. 125 per \( m^2 \), we can find the total cost by multiplying the area of the path by the cost per square meter.

Calculating the cost:
\[ \text{Cost} = \text{Area of the path} \times \text{Cost per } m^2 \]
\[ \text{Cost} = 524 \, \text{m}^2 \times 125 \, \text{Rs/m}^2 = 65500 \, \text{Rs} \]

### Final Answer:
- Area of the path: 524 \( m^2 \)
- Cost of constructing the path: Rs. 65500

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