# Maximum Ratio of Areas

Geometry Level 5

Let $$T$$ be an acute-angled triangle, and $$R$$,$$S$$ be rectangles inscribed in it as shown. If $$A(x)$$ denotes the area of the figure $$x$$, the maximum value of $$\displaystyle \dfrac{A(R)+A(S)}{A(T)}$$ can be expressed as $$\dfrac{P}{Q}$$, where $$P,Q$$ are coprime positive integers. Find the maximum possible area of a triangle with $$P$$, $$Q$$ as two of it's sides.

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