# Find maximum area of rectangle

Calculus Level 4

A rectangle's bottom is at $$y=0$$

while its top corners are on the curve $$y=x{ (x-1) }^{ 2 }$$ between $$x=0$$ and $$x=1$$. The maximum area of this rectangle can be expressed as

$\dfrac { a\sqrt { a } -b }{ c\sqrt { d } }$

where $$a$$ and $$d$$ are prime numbers. What is the sum $$a+b+c+d?$$

(Don't count $$a$$ twice)

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