# Just a slice, please .....

Consider a rectangle with vertices $$(0,0), (7,0), (0,5)$$ and $$(7,5)$$.

Next, of the set of lines that slice this rectangle into two sections, choose a line at random, (uniformly distributed over the angle $$\theta$$ the line makes with the positive $$x$$-axis).

The expected value for the area of the smaller of the two sections that the rectangle is divided into by the chosen line can be expressed as $$\frac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers. Find $$a + b$$.

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