A Maximal Square

Geometry Level 5

Let a be the side length of a regular pentagon, and let b be the side length of the largest square that can be inscribed in that pentagon. Find the value of \(\lfloor 1000 \frac{a}{b} \rfloor\).

(The floor function \(\lfloor x \rfloor\) gives the greatest integer less than or equal to the real number x.)

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