# Longest side is in interval

Geometry Level pending

If $$a$$, $$b$$, and $$c$$ are three sides of a triangle, then the value of $$\max (a,b,c)$$ is in the interval $$[p(a+b+c),q(a+b+c))$$. If $$p+q$$ can be expressed as $$\dfrac{x}{y}$$, where $$x$$ and $$y$$ are relative primes, find $$x+y$$.

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