A side of a square plot is 150 m long. Inside the plot, 3.5 m wide path is constructed all around the sides. The area of the path is :

Question

Accepted Answer

To determine the area of the path constructed around the square plot, we need to follow these steps:

1. **Calculate the Area of the Original Square Plot:**
   - The side of the square plot is given as 150 meters.
   - The area of the square plot is calculated using the formula: Area = side × side.
   - Therefore, the area of the original square plot = 150 m × 150 m = 22,500 square meters.

2. **Calculate the Side Length of the Inner Square (Excluding the Path):**
   - The path is 3.5 meters wide and is constructed all around the plot.
   - This means the path reduces the length of each side of the inner square by 2 × 3.5 m = 7 m (3.5 m on each side).
   - Therefore, the side length of the inner square = 150 m - 7 m = 143 m.

3. **Calculate the Area of the Inner Square:**
   - The area of the inner square is calculated using the formula: Area = side × side.
   - Therefore, the area of the inner square = 143 m × 143 m = 20,449 square meters.

4. **Calculate the Area of the Path:**
   - The area of the path is the difference between the area of the original square plot and the area of the inner square.
   - Area of the path = Area of the original square plot - Area of the inner square
   - Area of the path = 22,500 sq. m. - 20,449 sq. m. = 2,051 sq. m.

Therefore, the area of the path is 2,051 square meters, which corresponds to Option 4.

**Explanation for Incorrect Options:**

- **Option 1 (2100 sq. m.):** This option overestimates the area of the path. The correct calculation shows that the area is 2,051 sq. m., not 2,100 sq. m.
  
- **Option 2 (2002 sq. m.):** This option underestimates the area of the path. The correct calculation shows that the area is 2,051 sq. m., not 2,002 sq. m.

- **Option 3 (2151 sq. m.):** This option also overestimates the area of the path. The correct calculation shows that the area is 2,051 sq. m., not 2,151 sq. m.

In conclusion, the correct answer is Option 4, which accurately reflects the calculated area of the path as 2,051 square meters.