The percentage increase in the area of a rectangle, if each if its sides is increased by 20% , is :

Options

A. `40%`
B. `42%`
C. `44%`
D. `46%`

Answer

To find the percentage increase in the area of a rectangle when each of its sides is increased by 20%, we can follow these steps:

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

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

### Step 3: Determine the new dimensions after the increase.
If each side is increased by 20%, the new length \( L' \) and new width \( W' \) can be calculated as follows:
\[ L' = L + 0.2L = 1.2L \]
\[ W' = W + 0.2W = 1.2W \]

### Step 4: Calculate the new area of the rectangle.
The new area \( A' \) after the increase in dimensions is:
\[ A' = L' \times W' = (1.2L) \times (1.2W) = 1.44LW \]

### Step 5: Calculate the increase in area.
The increase in area can be found by subtracting the original area from the new area:
\[ \text{Increase in Area} = A' - A = 1.44LW - LW = 0.44LW \]

### Step 6: Calculate the percentage increase in area.
The percentage increase in area is given by the formula:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Area}}{\text{Original Area}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Increase} = \left( \frac{0.44LW}{LW} \right) \times 100 = 44\% \]

### Final Answer:
The percentage increase in the area of the rectangle when each side is increased by 20% is **44%**.

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