A rectangular park is 25 m long and 15 m wide. A path 3 m is constructed outside the park. Find the area of the path.

Options

A. `277 m^(2)`
B. `276 m^(2)`
C. `266 m^(2)`
D. `256 m^(2)`

Answer

To find the area of the path constructed outside the rectangular park, we will follow these steps:

### Step 1: Calculate the area of the park
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]
For the park:
- Length = 25 m
- Width = 15 m

Calculating the area:
\[ \text{Area of the park} = 25 \, \text{m} \times 15 \, \text{m} = 375 \, \text{m}^2 \]

### Step 2: Calculate the dimensions of the park including the path
The path is 3 m wide and surrounds the park. Therefore, the length and width of the park including the path will be increased by 3 m on each side.

New length:
\[ \text{New Length} = 25 \, \text{m} + 3 \, \text{m} + 3 \, \text{m} = 25 \, \text{m} + 6 \, \text{m} = 31 \, \text{m} \]

New width:
\[ \text{New Width} = 15 \, \text{m} + 3 \, \text{m} + 3 \, \text{m} = 15 \, \text{m} + 6 \, \text{m} = 21 \, \text{m} \]

### Step 3: Calculate the area of the park including the path
Now, we can calculate the area of the larger rectangle (park + path):
\[ \text{Area of the park including the path} = \text{New Length} \times \text{New Width} = 31 \, \text{m} \times 21 \, \text{m} \]

Calculating the area:
\[ \text{Area} = 31 \, \text{m} \times 21 \, \text{m} = 651 \, \text{m}^2 \]

### Step 4: Calculate the area of the path
To find the area of the path alone, we subtract the area of the park from the area of the park including the path:
\[ \text{Area of the path} = \text{Area of the park including the path} - \text{Area of the park} \]
\[ \text{Area of the path} = 651 \, \text{m}^2 - 375 \, \text{m}^2 = 276 \, \text{m}^2 \]

### Final Answer
The area of the path is:
\[ \text{Area of the path} = 276 \, \text{m}^2 \]

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