A man walking diagonally across a square lot saves approximately 30% of the distance compared to walking along the edges. Here's the reasoning:

• Let the side length of the square be xxx.
• Walking along the edges means covering two sides: 2x2x2x.
• Walking diagonally means covering the diagonal, which by the Pythagorean theorem is x2x\sqrt{2}x2​.
• The distance saved is 2x−x2=x(2−2)2x-x\sqrt{2}=x(2-\sqrt{2})2x−x2​=x(2−2​).
• The percentage saved is 2x−x22x×100=(1−22)×100\frac{2x-x\sqrt{2}}{2x}\times 100=(1-\frac{\sqrt{2}}{2})\times 1002x2x−x2​​×100=(1−22​​)×100.
• Since 2≈1.414\sqrt{2}\approx 1.4142​≈1.414, the percentage saved is approximately (1−0.707)×100=29.3%(1-0.707)\times 100=29.3%(1−0.707)×100=29.3%, which rounds to about 30%.

Therefore, the man saves roughly 30% of the distance by walking diagonally across the square lot instead of along the edges