What is the ratio of the area of the smallest equilateral triangle to the largest equilateral triangle that can fit inside a unit square?

The smallest equilateral triangle that can be drawn inside a unit square has sides equal to unity and area equal to \(a\) .

The largest equilateral triangle that can fit inside a unit square has sides of length \(s\) and area equal to \(b\).

Find \(\frac ab\) correct to 3 decimal places.

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