The length and breadth of a rectangular field are both increased by 20%. By what % is the area increased?

Options

A. `20%`
B. `30%`
C. `44%`
D. `40%`

Explanation

To solve the problem of how much the area of a rectangular field increases when both its length and breadth are increased by 20%, we can follow these steps:

### Step 1: Understand the Original Dimensions
Let the original length of the rectangle be \( L \) and the original breadth be \( B \). The area \( A \) of the rectangle can be calculated using the formula:
\[ A = L \times B \]

### Step 2: Calculate the New Dimensions
Since both the length and breadth are increased by 20%, we can express the new dimensions as follows:
- New Length \( L' = L + 0.2L = 1.2L \)
- New Breadth \( B' = B + 0.2B = 1.2B \)

### Step 3: Calculate the New Area
Now, we can calculate the new area \( A' \) using the new dimensions:
\[ A' = L' \times B' = (1.2L) \times (1.2B) = 1.44LB \]

### Step 4: Calculate the Increase in Area
To find the increase in area, we subtract the original area from the new area:
\[ \text{Increase in Area} = A' - A = 1.44LB - LB = 0.44LB \]

### Step 5: Calculate the Percentage Increase in Area
To find the percentage increase in area, we use the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Area}}{\text{Original Area}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Increase} = \left( \frac{0.44LB}{LB} \right) \times 100 = 44\% \]

### Conclusion
Thus, the area of the rectangular field is increased by **44%**.

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