The length of a rectangle is halved while its breadth is tripled. What is the percentage change in area?

Problem restatementFind how the area changes when L → L/2 and B → 3B.

Given data

• Original area = L × B.
• New area = (L/2) × (3B).

Concept/ApproachArea scales by the product of the scale factors.

Step-by-Step calculation New area = (L × B) × (1/2) × 3 = (3/2)LB = 1.5 × original area ⇒ 50% increase

Common pitfalls

• Adding percentage changes (−50% and +200%) incorrectly; use multiplicative scaling.

Final Answer50% increase