The length of a rectangle is halved while its breadth is tripled. Compared to the original rectangle, what is the percentage change in its area? (State whether it increases or decreases.)

Introduction / Context:
This question tests how area changes when dimensions scale. For a rectangle, area = length * breadth. If length and breadth are multiplied by certain factors, the area is multiplied by the product of those factors. Then the percentage change can be found by comparing new area to old area.

Given Data / Assumptions:

• Original length = L
• Original breadth = B
• Original area = L*B
• New length = L/2 (halved)
• New breadth = 3B (tripled)

Concept / Approach:
New area = (L/2) * (3B) = (3/2) * (L*B). This means the new area is 1.5 times the old area, i.e., a 50% increase.

Step-by-Step Solution:
Original area A1 = L*B New area A2 = (L/2) * (3B) = (3/2) * L*B So A2/A1 = 3/2 = 1.5 Increase factor = 1.5 - 1 = 0.5 Percentage increase = 0.5*100% = 50% increase

Verification / Alternative check:
Example check: let L = 10, B = 4, old area = 40. New length = 5, new breadth = 12, new area = 60. Increase = 20, and 20/40 = 50% increase, confirming the result.

Why Other Options Are Wrong:
20%, 30%, 40% increase: these would require a different scaling factor, not 1.5. 50% decrease: opposite direction; the area increases because tripling breadth dominates halving length.

Common Pitfalls:
Adding scaling factors instead of multiplying them. Assuming halving one dimension always decreases area, ignoring the other dimension change. Computing 3/2 as 2/3 by mistake.

Final Answer:
The area shows a 50% increase