The length of a rectangle is increased by 10% and the breadth is increased by 25%. What is the percentage change in its area?

Options

A. Increase of 37.5%
B. Decrease of 25%
C. Decrease of 37.5%
D. Increase of 25%

Answer

To solve the problem of finding the percentage change in the area of a rectangle when its length and breadth are increased, 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 area \( A \) of a rectangle is given by the formula:
\[ A = L \times B \]
So, the original area \( A_1 \) is:
\[ A_1 = L \times B \]

### Step 3: Calculate the new dimensions after the increase
- The length is increased by 10%, so the new length \( L' \) is:
\[ L' = L + 0.10L = 1.10L \]
- The breadth is increased by 25%, so the new breadth \( B' \) is:
\[ B' = B + 0.25B = 1.25B \]

### Step 4: Calculate the new area
The new area \( A_2 \) after the increases in dimensions is:
\[ A_2 = L' \times B' = (1.10L) \times (1.25B) \]
Calculating this gives:
\[ A_2 = 1.10 \times 1.25 \times L \times B = 1.375 \times (L \times B) = 1.375A_1 \]

### Step 5: Calculate the change in area
The change in area is:
\[ \Delta A = A_2 - A_1 = 1.375A_1 - A_1 = 0.375A_1 \]

### Step 6: Calculate the percentage change in area
The percentage change in area is given by:
\[ \text{Percentage Change} = \left( \frac{\Delta A}{A_1} \right) \times 100 = \left( \frac{0.375A_1}{A_1} \right) \times 100 = 37.5\% \]

### Final Answer
The percentage change in the area of the rectangle is **37.5%**.

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