A landowner increased the length and breadth of a rectangular plot by 10% and 20% respectively. Find the percentage change in the Area of the plot.

Options

A. 35%
B. 33%
C. 22%
D. 32%

Answer

To find the percentage change in the area of a rectangular plot when the length and breadth are increased by 10% and 20% respectively, we can follow these steps:

### Step 1: Define the original dimensions
Let the original length of the rectangle be \( L \) and the original breadth be \( B \).

### Step 2: Calculate the new dimensions
- The new length after a 10% increase:
\[ \text{New Length} = L + 0.10L = 1.10L \]
- The new breadth after a 20% increase:
\[ \text{New Breadth} = B + 0.20B = 1.20B \]

### Step 3: Calculate the original area
The original area \( A \) of the rectangle is given by:
\[ A = L \times B \]

### Step 4: Calculate the new area
The new area \( A' \) after the increases in length and breadth is:
\[ A' = \text{New Length} \times \text{New Breadth} = (1.10L) \times (1.20B) \]
Calculating this gives:
\[ A' = 1.10 \times 1.20 \times L \times B = 1.32 \times (L \times B) = 1.32A \]

### Step 5: Calculate the percentage change in area
The percentage change in area can be calculated using the formula:
\[ \text{Percentage Change} = \left( \frac{A' - A}{A} \right) \times 100 \]
Substituting the values we found:
\[ \text{Percentage Change} = \left( \frac{1.32A - A}{A} \right) \times 100 = \left( \frac{0.32A}{A} \right) \times 100 = 32\% \]

### Conclusion
The percentage change in the area of the plot is **32%**.

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