A square is transformed into a rectangle: Its length and breadth become 30% and 20% more than the original square’s side, respectively. By what percentage does the new rectangle’s area exceed the original square’s area?

Introduction / Context:
We compare the area of a square with that of a rectangle formed by increasing the side in two perpendicular directions by different percentages. This is a standard compound-change area problem using multiplicative factors.

Given Data / Assumptions:
Square side = s. Rectangle length = 1.30s. Rectangle breadth = 1.20s.

Concept / Approach:
Original area = s^2. New area = (1.30s) * (1.20s) = 1.56 * s^2. The area therefore increases by a factor of 1.56 relative to the original, which corresponds to a 56% increase.

Step-by-Step Solution:

Verification / Alternative check:
Assume s = 10 units; old area = 100. New area = 13 * 12 = 156. Excess = 56 over 100 ⇒ 56%.

Why Other Options Are Wrong:
36% and 50% mis-handle multiplicative compounding. 20% is far too small. 60% rounds up incorrectly.

Common Pitfalls:
Adding 30% + 20% and stopping at 50% without compounding. Always multiply the separate scale factors for perpendicular dimensions.

Final Answer:
56%