If the length of a rectangle is increased by 30% and its width is increased by 10%, by what percentage will be the area of the rectangle be increased?

Options

A. 0.33
B. 0.37
C. 0.4
D. 0.43

Answer

To solve the problem step by step, we will calculate the new dimensions of the rectangle after the increases, find the new area, and then determine the percentage increase in the area.

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

### Step 2: Calculate the original area
The original area \( A \) of the rectangle is given by:
\[ A = L \times W \]

### Step 3: Calculate the new length
The length is increased by 30%. Therefore, the new length \( L_1 \) can be calculated as:
\[ L_1 = L + 0.3L = 1.3L \]

### Step 4: Calculate the new width
The width is increased by 10%. Therefore, the new width \( W_1 \) can be calculated as:
\[ W_1 = W + 0.1W = 1.1W \]

### Step 5: Calculate the new area
The new area \( A_1 \) of the rectangle is given by:
\[ A_1 = L_1 \times W_1 = (1.3L) \times (1.1W) = 1.43LW \]

### Step 6: Calculate the increase in area
The increase in area is given by:
\[ \text{Increase in Area} = A_1 - A = 1.43LW - LW = 0.43LW \]

### Step 7: Calculate the percentage increase in area
The percentage increase in area can be calculated as:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Area}}{\text{Original Area}} \right) \times 100 = \left( \frac{0.43LW}{LW} \right) \times 100 = 43\% \]

### Final Answer
The area of the rectangle will be increased by **43%**.

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