# 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*.)