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

Options

A. increases by 5%
B. decreases by 5%
C. remains unchanged
D. increases by 10%

Answer

To solve the problem step by step, we need to analyze the changes in the dimensions of the rectangle and how they affect the area.

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

### Step 2: Calculate the new dimensions
- The length is increased by 25%. Therefore, the new length \( L' \) can be calculated as:
\[ L' = L + 0.25L = 1.25L \]

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

### Step 3: Calculate the original area
The original area \( A \) of the rectangle is given by:
\[ A = L \times W \]

### Step 4: Calculate the new area
The new area \( A' \) of the rectangle after the changes is:
\[ A' = L' \times W' = (1.25L) \times (0.80W) \]
\[ A' = 1.25 \times 0.80 \times L \times W \]
\[ A' = 1.00 \times L \times W \]
\[ A' = A \]

### Step 5: Determine the change in area
The change in area can be calculated as:
\[ \text{Change in Area} = A' - A = A - A = 0 \]

### Conclusion
The area of the rectangle remains unchanged after the changes in length and width.

### Final Answer
The area of the rectangle does not change, which means the percentage change in area is 0%.

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