# 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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