A man walks diagonally across a square plot instead of along two edges. Approximately what percentage distance is saved by taking the diagonal path?

Introduction / Context:Distance saved equals (edge path − diagonal) / edge path. In a square of side s, the edge path from one corner to the opposite via two sides is 2s, while the straight diagonal distance is s√2.

Given Data / Assumptions:

• Square side = s (symbolic; cancels out).

Concept / Approach:Compute percent saving = [(2s − s√2) / (2s)] * 100% = [1 − (√2)/2]*100%.

Step-by-Step Solution:

Verification / Alternative check:Set s = 1. Edge path = 2, diagonal ≈ 1.4142, saving ≈ 0.5858 ≈ 29.3% of 2.

Why Other Options Are Wrong:

• 10%, 20%: Underestimates.
• 40%: Overestimates.

Final Answer:30%