The length of a rectangle is increased by 25% and its breadth is decreased by 25%.  Find the percentage change in its area.

To find the percentage change in the area of a rectangle when its length is increased by 25% and its breadth is decreased by 25%, follow these steps:

### Step 1: Let the original length and breadth be \( l \) and \( b \).
- The original area \( A_1 \) of the rectangle is:
  \[
  A_1 = l \times b
  \]

### Step 2: Calculate the new length and breadth.
- New length \( l' \) after a 25% increase:
  \[
  l' = l \times \left(1 + \frac{25}{100}\right) = l \times 1.25
  \]
- New breadth \( b' \) after a 25% decrease:
  \[
  b' = b \times \left(1 - \frac{25}{100}\right) = b \times 0.75
  \]

### Step 3: Calculate the new area \( A_2 \) with the adjusted dimensions.
\[
A_2 = l' \times b' = (l \times 1.25) \times (b \times 0.75) = 1.25 \times 0.75 \times l \times b
\]
\[
A_2 = 0.9375 \times l \times b
\]

### Step 4: Find the percentage change in the area.
- The percentage change in area is calculated as:
  \[
  \text{Percentage change} = \frac{A_2 - A_1}{A_1} \times 100
  \]
  Substituting the values:
  \[
  \text{Percentage change} = \frac{0.9375 \times l \times b - l \times b}{l \times b} \times 100
  \]
  \[
  \text{Percentage change} = \frac{0.9375 - 1}{1} \times 100 = -0.0625 \times 100 = -6.25\%
  \]

### Final Answer:
The area of the rectangle decreases by **6.25%**.

Would you like further clarification or have any additional questions?

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Here are some related questions:

1. What happens to the area if both length and breadth are increased by 25%?
2. How do you calculate the new area if only the length is increased by 10% and the breadth remains the same?
3. What is the formula for finding the area of a rectangle?
4. Can the area of a rectangle ever be negative?
5. How would the percentage change in area be different if the length increased by 50% and the breadth decreased by 50%?
6. What is the effect on area if both the length and breadth decrease by the same percentage?
7. How do you apply percentage change to other geometric shapes, like a triangle?
8. Can you use the same method to find the percentage change in volume for a rectangular prism?

**Tip:** Always keep track of whether a change is an increase or a decrease; it directly affects whether the final result will show an increase or decrease in the calculated area or value.

Learn how to calculate the percentage change in the area of a rectangle when its length is increased by 25% and its breadth is decreased by 25%. Follow a step-by-step solution with detailed formulas and calculations. Suitable for Grades 7-9.

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