If the length of a rectangle is increased by 20% and breadth is increased by 30%, then what will be the percentage increase in the area of rectangle ?

Options

A. 50
B. 46
C. 56
D. 62

Answer

To solve the problem of finding the percentage increase in the area of a rectangle when its length and breadth are increased by certain percentages, 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 length is increased by 20%. Therefore, the new length \( L' \) is given by:
\[ L' = L + 0.20L = 1.20L \]
- The breadth is increased by 30%. Therefore, the new breadth \( B' \) is given by:
\[ B' = B + 0.30B = 1.30B \]

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

### Step 4: Calculate the new area
The new area \( A' \) after the increases in dimensions is:
\[ A' = L' \times B' = (1.20L) \times (1.30B) \]
\[ A' = 1.20 \times 1.30 \times L \times B \]
\[ A' = 1.56 \times A \]

### Step 5: Calculate the increase in area
The increase in area is:
\[ \text{Increase in Area} = A' - A = 1.56A - A = 0.56A \]

### Step 6: Calculate the percentage increase in area
The percentage increase in area is given by:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Area}}{\text{Original Area}} \right) \times 100 \]
\[ \text{Percentage Increase} = \left( \frac{0.56A}{A} \right) \times 100 = 56\% \]

### Final Answer
The percentage increase in the area of the rectangle is **56%**.

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