A man walks from one corner of a square plot to the opposite corner. Approximately what percent distance is saved by walking diagonally instead of walking along two sides (along the edges)?

Introduction / Context:
This question tests understanding of a square’s diagonal and comparing two travel paths. If the square has side s, walking along the edges from one corner to the opposite corner requires walking two sides: distance = s + s = 2s. Walking diagonally uses the square’s diagonal, which is s*sqrt(2) by the Pythagoras theorem. The “percent saved” is computed as: (saved distance / original distance) * 100, where “original distance” is the along-the-edges distance 2s, and “saved distance” is (2s - s*sqrt(2)). Because sqrt(2) is approximately 1.414, the savings becomes a percentage close to 29.3%, which is usually rounded to about 30% in aptitude options.

Given Data / Assumptions:

• Square side length = s
• Edge path distance (two sides) = 2s
• Diagonal distance = s*sqrt(2)
• Percent saved = ((2s - s*sqrt(2)) / (2s)) * 100
• Use sqrt(2) ≈ 1.414 for approximation

Concept / Approach:
Compute the fractional saving: (2 - sqrt(2)) / 2, then convert to percent and round to the nearest option.

Step-by-Step Solution:
Edge distance = 2s Diagonal distance = s*sqrt(2) Saved distance = 2s - s*sqrt(2) = s*(2 - sqrt(2)) Fraction saved = (s*(2 - sqrt(2))) / (2s) = (2 - sqrt(2)) / 2 Using sqrt(2) ≈ 1.414: (2 - 1.414) / 2 = 0.586 / 2 = 0.293 Percent saved ≈ 0.293 * 100 = 29.3% ≈ 30%

Verification / Alternative check:
Try s=100 m. Edge distance = 200 m. Diagonal ≈ 141.4 m. Saved ≈ 58.6 m. Percent saved ≈ 58.6/200*100 = 29.3%, confirming the same result numerically.

Why Other Options Are Wrong:
10% and 20% underestimate the diagonal advantage. 40% overestimates savings; diagonal is not half of 2s. 25% is a common guess but does not match the sqrt(2) based computation.

Common Pitfalls:
Comparing diagonal to one side (s) instead of two sides (2s), forgetting to divide by the original distance when converting to percent, or using an incorrect value for sqrt(2).

Final Answer:
Approximately 30% distance is saved by walking diagonally.