Question

The percentage change in area of a rectangle by decreasing its length and increasing its breadth by 5% is:

• A. no change
• B. 0.25% decrease
• C. 2.5% increase
• D. 0.25% increase

Hint:

When the dimensions of a rectangle change by a certain percentage, use the product of the percentage changes in length and breadth to calculate the overall change in area.

Answer 1

The Correct Option is B

Step 1: Understand the change in area.
Let the original length of the rectangle be \( L \) and the original breadth be \( B \). The original area \( A = L \times B \). Now, the length is decreased by 5%, and the breadth is increased by 5%. The new length is \( 0.95L \) and the new breadth is \( 1.05B \). The new area is: \[ A' = 0.95L \times 1.05B = 0.9975LB. \]

Step 2: Calculate the percentage change in area.
The percentage change in area is given by: \[ \text{Percentage change} = \frac{A' - A}{A} \times 100 = \frac{0.9975LB - LB}{LB} \times 100 = \frac{-0.0025LB}{LB} \times 100 = -0.25%. \]

Step 3: Conclusion.
Thus, the percentage change in area is a decrease of 0.25%. The correct answer is (b).