If length of a rectangle is increased by 10% and breadth is increased by 15%, then what will be the percentage increase in the area of rectangle ?

Options

A. `25.5`
B. 25
C. `28.4`
D. `26.5`

Answer

To solve the problem of finding the percentage increase in the area of a rectangle when its length is increased by 10% and its breadth is increased by 15%, we can follow these steps:

### Step-by-Step Solution:

1. **Let the Original Dimensions be Defined:**
- Let the original length of the rectangle be \( L = 10 \) units.
- Let the original breadth of the rectangle be \( B = 20 \) units.

2. **Calculate the Original Area:**
- The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]
- So, the original area \( A_1 \) is:
\[ A_1 = L \times B = 10 \times 20 = 200 \text{ square units} \]

3. **Calculate the New Dimensions After Increase:**
- The length is increased by 10%:
\[ \text{New Length} = L + 0.1L = 10 + 1 = 11 \text{ units} \]
- The breadth is increased by 15%:
\[ \text{New Breadth} = B + 0.15B = 20 + 3 = 23 \text{ units} \]

4. **Calculate the New Area:**
- The new area \( A_2 \) is:
\[ A_2 = \text{New Length} \times \text{New Breadth} = 11 \times 23 = 253 \text{ square units} \]

5. **Calculate the Increase in Area:**
- The increase in area is:
\[ \text{Increase in Area} = A_2 - A_1 = 253 - 200 = 53 \text{ square units} \]

6. **Calculate the Percentage Increase in Area:**
- The percentage increase in area is given by:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Area}}{\text{Original Area}} \right) \times 100 \]
- Substituting the values:
\[ \text{Percentage Increase} = \left( \frac{53}{200} \right) \times 100 = 26.5\% \]

### Final Answer:
The percentage increase in the area of the rectangle is **26.5%**.

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