Shortest route across a square plot: A man walks diagonally across a square instead of along two edges. Approximately what percentage distance does he save?

Introduction / Context:Walking along two sides of a square versus walking across the diagonal compares 2s and s*sqrt(2) distances (s = side).

Given Data / Assumptions:Square with side s; edge-route = 2s; diagonal = s*sqrt(2).

Concept / Approach:Percent saved = (edge − diagonal) / edge * 100% = (2s − s√2) / (2s) * 100%.

Step-by-Step Solution:

Verification / Alternative check:Take s = 100 → edge 200; diagonal ≈ 141.42; saved ≈ 58.58 ≈ 29.3%.

Why Other Options Are Wrong:10%, 20%, 40% are common round guesses; the computed saving is about 30%.

Common Pitfalls:Using √2 ≈ 1.4 too coarsely; the accepted approximation yields ~30%.

Final Answer:30%