A rectangle’s length is increased by 60% (to 1.6L). By what percentage must its width be decreased to keep the area unchanged?

Introduction / Context:
Keeping area constant under one-dimensional scaling requires inversely scaling the other dimension. If length increases, width must decrease so that the product length * width remains the same.

Given Data / Assumptions:

• Original dimensions: L and W
• New length L′ = 1.6L
• Area constant: L′ * W′ = L * W

Concept / Approach:
From L′ * W′ = L * W, we get W′ = (L * W) / L′ = W / 1.6 = 0.625W. This corresponds to a 37.5% decrease from W (since 1 − 0.625 = 0.375 = 37.5%).

Step-by-Step Solution:
Scale factor for width = 1 / 1.6 = 0.625Decrease = (1 − 0.625) × 100% = 37.5% = 37 1/2%

Verification / Alternative check:
Test with numbers: L = 10, W = 10 ⇒ area = 100. Increase L by 60% ⇒ L′ = 16. Reduce W by 37.5% ⇒ W′ = 6.25. New area = 16 * 6.25 = 100 — unchanged.

Why Other Options Are Wrong:
60% and 75% overshoot, destroying area equality; 120% is nonsensical for a decrease. Only 37 1/2% preserves equality.

Common Pitfalls:
Subtracting 60% directly from width or misapplying percentage decrease; always use reciprocal scaling to keep the product fixed.

Final Answer:
37 1/2%