If the length of a rectangle is increased by 25% and the width is decreased by 20%, then the area of rectangle will be

Options

A. increase by 5%
B. decrease by 5%
C. remains unchanged
D. increased by 10%

Answer

To solve the problem, we need to find the new area of the rectangle after the changes in length and width. Let's break it down step by step.

### 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 new length
The length of the rectangle is increased by 25%. Therefore, the new length \( L' \) can be calculated as:
\[ L' = L + 0.25L = 1.25L \]

### Step 3: Calculate the new width
The width of the rectangle is decreased by 20%. Therefore, the new width \( W' \) can be calculated as:
\[ W' = W - 0.20W = 0.80W \]

### Step 4: Calculate the new area
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]
Thus, the new area \( A' \) of the rectangle can be calculated as:
\[ A' = L' \times W' = (1.25L) \times (0.80W) \]

### Step 5: Simplify the expression for the new area
Now, we can simplify the expression:
\[ A' = 1.25 \times 0.80 \times L \times W \]
Calculating \( 1.25 \times 0.80 \):
\[ 1.25 \times 0.80 = 1.00 \]
Thus,
\[ A' = 1.00 \times L \times W = L \times W \]

### Step 6: Conclusion
The new area \( A' \) is equal to the original area \( A \) of the rectangle. Therefore, the area of the rectangle remains unchanged.