Square Inscribed Triangle

Geometry Level 4

The area of Square \(\Box DEFG\) is \(a\sqrt{b}-c\), which is inscribed into an equilateral \(\triangle ABC\).

With \(a,b,c\) are all integers and \(b\) square free. And The area of the equilateral triangle \(\triangle ABC\) is \(1\).

Evaluate \(\dfrac{c-a}{b}\) to three decimal places.

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