A rectangular garden is 124m long and 92 m wide. Find the cost of making a 3-m wide path araound it at the rate of Rs 160 per sq. m .

Answer

To solve the problem of finding the cost of making a 3-meter wide path around a rectangular garden that is 124 m long and 92 m wide, we can follow these steps:

### Step 1: Calculate the area of the rectangular garden.
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]
For the garden:
\[ \text{Area of the garden} = 124 \, \text{m} \times 92 \, \text{m} = 11,408 \, \text{m}^2 \]

### Step 2: Calculate the dimensions of the garden including the path.
Since the path is 3 m wide on all sides, we need to add 6 m to both the length and the width (3 m on each side).
\[ \text{New Length} = 124 \, \text{m} + 6 \, \text{m} = 130 \, \text{m} \]
\[ \text{New Width} = 92 \, \text{m} + 6 \, \text{m} = 98 \, \text{m} \]

### Step 3: Calculate the area of the garden including the path.
Now, we can calculate the area of the larger rectangle (garden + path):
\[ \text{Area of the garden with path} = 130 \, \text{m} \times 98 \, \text{m} = 12,740 \, \text{m}^2 \]

### Step 4: Calculate the area of the path alone.
To find the area of the path, we subtract the area of the garden from the area of the garden with the path:
\[ \text{Area of the path} = \text{Area of the garden with path} - \text{Area of the garden} \]
\[ \text{Area of the path} = 12,740 \, \text{m}^2 - 11,408 \, \text{m}^2 = 1,332 \, \text{m}^2 \]

### Step 5: Calculate the cost of making the path.
The cost of making the path is given by multiplying the area of the path by the cost per square meter:
\[ \text{Cost} = \text{Area of the path} \times \text{Cost per sq. m} \]
\[ \text{Cost} = 1,332 \, \text{m}^2 \times 160 \, \text{Rs/m}^2 = 2,13,120 \, \text{Rs} \]

### Final Answer:
The cost of making the 3-meter wide path around the garden is Rs 2,13,120.

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