Every triangle

Geometry Level 5

Within a square, suppose that every third of its perimeter is connected to form a triangle. Let \(x\) be the ratio of the area of the triangle to the square. If the difference of the maximum and minimum value of \(x\) can be expressed in the form \( \large \frac {a}{b}\), where \(a\) and \(b\) are coprime positive integers, determine the value of

\( 3 \times (a + b) \).

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