If length and breadth of a rectangle are increased by 15% and 20% respectively, then what will be the percentage increase in area ?

Options

A. 37
B. 40
C. 35
D. 38

Answer

To find the percentage increase in the area of a rectangle when its length and breadth are increased by 15% 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 original area
The original area \( A \) of the rectangle can be calculated using the formula:
\[ A = L \times B \]

### Step 3: Calculate the new dimensions
- The new length after a 15% increase is:
\[ L' = L + 0.15L = 1.15L \]
- The new breadth after a 20% increase is:
\[ B' = B + 0.20B = 1.20B \]

### Step 4: Calculate the new area
The new area \( A' \) of the rectangle can be calculated using the new dimensions:
\[ A' = L' \times B' = (1.15L) \times (1.20B) \]
\[ A' = 1.15 \times 1.20 \times L \times B \]
\[ A' = 1.38 \times (L \times B) \]

### Step 5: Calculate the percentage increase in area
The percentage increase in area can be calculated using the formula:
\[ \text{Percentage Increase} = \left( \frac{A' - A}{A} \right) \times 100 \]
Substituting the values we found:
\[ \text{Percentage Increase} = \left( \frac{1.38AB - AB}{AB} \right) \times 100 \]
\[ = \left( \frac{0.38AB}{AB} \right) \times 100 \]
\[ = 0.38 \times 100 = 38\% \]

### Conclusion
The percentage increase in the area of the rectangle is **38%**.

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