# Ratio of the area of the Smallest to the Largest Equilateral triangle in a unit square

Geometry Level 4

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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