A man walked diagonally across a square lot instead of walking along two edges (first along one side and then along the adjacent side). Approximately what percentage distance did he save by walking along the diagonal?

Introduction:
This question tests the geometry of a square and compares two path lengths: walking along the edges versus walking along the diagonal. For a square of side s, walking along two sides (edges) to go from one corner to the opposite corner is a distance of 2s. Walking directly across the diagonal is s*sqrt(2) by the Pythagorean relation. The percentage saved is computed by comparing the difference to the original (edge) path. Because sqrt(2) is an irrational number, the final answer is approximate.

Given Data / Assumptions:

• Square side length = s• Distance along edges (two sides) = 2s• Diagonal distance = s*sqrt(2)

Concept / Approach:
Percent saved = (original distance - new distance) / original distance * 100. Here, original distance is 2s and new distance is s*sqrt(2). The factor s cancels out, so the answer does not depend on the size of the square, only on sqrt(2).

Step-by-Step Solution:
Step 1: Write the two path lengths.Edges path = 2sDiagonal path = s*sqrt(2)Step 2: Compute saving as a fraction of edge path.Saved fraction = (2s - s*sqrt(2)) / (2s)= (s(2 - sqrt(2))) / (2s)= (2 - sqrt(2)) / 2Step 3: Convert to a decimal using sqrt(2) ≈ 1.414.Saved fraction ≈ (2 - 1.414)/2 = 0.586/2 = 0.293Step 4: Convert to percentage.Saved percentage ≈ 0.293 * 100 ≈ 29.3%Approximately 30%

Verification / Alternative check:
Let s=100 m. Along edges: 200 m. Diagonal: 100*1.414 = 141.4 m. Saving = 58.6 m. Percentage saved = 58.6/200*100 = 29.3%. Rounding gives about 30%, matching the option.

Why Other Options Are Wrong:
40%, 50%, and 60% would require the diagonal to be far shorter than it actually is.25% is too low; the actual computed saving is closer to 29%.30% is the closest approximate choice to 29.3%.

Common Pitfalls:
• Using sqrt(3) or another wrong value instead of sqrt(2) for the diagonal.• Dividing by diagonal distance instead of the original edge distance when computing percent saved.• Forgetting to multiply by 100 to convert a fraction to percentage.

Final Answer:
Approximately 30% distance is saved by walking along the diagonal.