Quite the Irrational Triangle

Geometry Level 4

Given the equation:

\(\frac { \sqrt { 2 } }{ rx-\pi } +\frac { \sqrt { 3 } }{ \phi y-e } =0\)

Find the area A of the triangle bounded by the function and the x and y axes and evaluate the following expression:

\(\sqrt { \left\lfloor 100\left[ \frac { A }{ \pi \phi e r} \right] \right\rfloor } \)


\(\pi\) is pi, the mathematical constant approximately equal to 3.1415

\(\phi\) is the golden ratio, approximately 1.618

r is the Dottie constant, approximately 0.739, and can be generated by repeatedly taking the cosine of any real number in radians.

e is Euler's number, approximately 2.71828

\(\left\lfloor \right\rfloor \) is the floor function.

Please use more exact values than given.


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