Maximizing Area/Perimeter

Geometry Level 3

Within a \( 100 \times 100 \) square, draw in a shape that maximizes the ratio \( \frac{ \text{ Area } } { \text{ Perimeter } } \).

What is this ratio (to 2 decimal places)?

For example, if we drew in a \( 100 \times 100 \) square, we would get \( \frac{ 100 ^ 2 } { 4 \times 100 } = 25 \).

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