# Bounding A Triangle

Geometry Level 4

For $$a> 0$$, the above diagram shows the vertical line $$x=a$$ bounds a triangle with the lines $$y=2x-1$$ and $$y = -\frac x2 + 1$$.

If the constraint $$a>0$$ is relaxed, then there is another possible value of $$a$$ such that the enclosed area of the new triangle is also 5.

If the sum of these two values of $$a$$ can be expressed as $$\dfrac BC$$, where $$B$$ and $$C$$ are coprime positive integers, find $$B+C$$.

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