A rectangular plot is given for constructing a house, having a measurement of 40 m long and 15 m in the front. According to the laws, a minimum of 3-m-wide space should be left in the front and back each and 2 m wide space on each of the other sides. Find the largest area where house can be constructed.

Explanation

To find the largest area where the house can be constructed on the given rectangular plot, we will follow these steps:

### Step 1: Understand the dimensions of the plot
The dimensions of the rectangular plot are given as:
- Length = 40 m
- Breadth = 15 m

### Step 2: Determine the space that needs to be left
According to the laws:
- A minimum of 3 m wide space should be left in the front and back.
- A minimum of 2 m wide space should be left on each of the other sides (left and right).

### Step 3: Calculate the effective dimensions for the house
1. **Calculate the effective length:**
- Total space to be left on the length side = 3 m (front) + 3 m (back) = 6 m
- Effective length = Original length - Total space left
- Effective length = 40 m - 6 m = 34 m

2. **Calculate the effective breadth:**
- Total space to be left on the breadth side = 2 m (left) + 2 m (right) = 4 m
- Effective breadth = Original breadth - Total space left
- Effective breadth = 15 m - 4 m = 11 m

### Step 4: Calculate the area where the house can be constructed
- Area = Effective length × Effective breadth
- Area = 34 m × 11 m = 374 m²

### Conclusion
The largest area where the house can be constructed is **374 m²**.

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