A rectangle’s length becomes half and its breadth becomes double. The resultant area is what percent of the original area?

Introduction / Context:
This problem examines how proportional changes in dimensions affect area. For rectangles, area equals length * breadth, so scaling factors multiply directly to give the new area factor.

Given Data / Assumptions:

• Original area A = L * B.
• New length L′ = (1/2) * L.
• New breadth B′ = 2 * B.

Concept / Approach:
The new area A′ equals L′ * B′. Substitute the scaled dimensions and compute the ratio A′/A. Convert that ratio to a percentage of the original area.

Step-by-Step Solution:
A′ = L′ * B′ = (1/2)L * (2B) = (1/2 * 2) * L * BA′ = 1 * L * B = ATherefore, A′/A = 1 ⇒ A′ is 100% of A

Verification / Alternative check:
Choose numbers: L = 10, B = 5 ⇒ A = 50. New: L′ = 5, B′ = 10 ⇒ A′ = 50. Same area confirms 100%.

Why Other Options Are Wrong:
75%, 80%, 55%, 25% would imply net shrinking; however, the halving and doubling exactly cancel out, leaving the area unchanged.

Common Pitfalls:
Adding percent changes (−50% + 100% = 50%) is incorrect because area depends on the product, not a sum. Always multiply the scale factors.

Final Answer:
100%