The Y/ X Ratio?

Geometry Level 3

If the formula for this figure's perimeter =(1+80.5)Y+(280.5)X=27.64= ( 1 + 8^{0.5}) Y + ( 2 - 8^{0.5} ) X = 27.64

and for this figure's area =(1+80.5)YX2+X21280.512=12.78 = \dfrac {( 1 + 8^{0.5} ) Y X} 2 + \dfrac {X^2} { 128^{0.5} - 12} = 12.78.

What does YX\dfrac Y X equal?

Give your answer to 3 decimal places.

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