The length and breadth of a rectangular field is 60 m and 40 m respectively. If on the outer of its four sides the grass of 5 metre width is planted, then the area of grass planted field is

Question

Accepted Answer

To determine the area of the grass-planted field, we need to calculate the total area of the field including the grass and then subtract the area of the original rectangular field.

1. **Original Field Dimensions:**
   - Length = 60 m
   - Breadth = 40 m

The area of the original rectangular field is:
   $$
   \text{Area of original field} = \text{Length} \times \text{Breadth} = 60 \, \text{m} \times 40 \, \text{m} = 2400 \, \text{sq.m}
   $$

2. **Grass-Planted Area:**
   - The grass is planted around the field with a width of 5 meters on all sides.
   - This means the length and breadth of the entire area including the grass will increase by 10 meters each (5 meters on each side).

New dimensions including the grass:
   - New Length = 60 m + 10 m = 70 m
   - New Breadth = 40 m + 10 m = 50 m

The area of the entire field including the grass is:
   $$
   \text{Area of field with grass} = \text{New Length} \times \text{New Breadth} = 70 \, \text{m} \times 50 \, \text{m} = 3500 \, \text{sq.m}
   $$

3. **Area of Grass-Planted Field:**
   - To find the area of the grass-planted field, subtract the area of the original field from the total area including the grass:
   $$
   \text{Area of grass} = \text{Area of field with grass} - \text{Area of original field} = 3500 \, \text{sq.m} - 2400 \, \text{sq.m} = 1100 \, \text{sq.m}
   $$

Therefore, the area of the grass-planted field is 1100 sq.m, which corresponds to Option 3.

**Explanation of Incorrect Options:**

- **Option 1 (1100 m):** This option incorrectly uses the unit "m" instead of "sq.m". The area should be expressed in square meters, not meters.
  
- **Option 2 (525 sq.m):** This option underestimates the area of the grass-planted field. The correct calculation shows that the area is 1100 sq.m, not 525 sq.m.
  
- **Option 4 (525 m):** Similar to Option 1, this option incorrectly uses the unit "m" instead of "sq.m". Additionally, the numerical value is incorrect as explained in Option 2.

Thus, Option 3 (1100 sq.m) is the correct answer, as it accurately represents the area of the grass-planted field.