# Ratio of Sides

Level pending

Triangle $$ABC$$ has side lengths $$a, b$$ and $$c$$ which satisfy $$\frac{a+b}{11}=\frac{b+c}{12}=\frac{c+a}{13}$$. If $$\sin A:\sin B:\sin C$$ can be expressed as an irreducible ratio $$p:q:r$$, where $$p$$, $$q$$ and $$r$$ are positive integers, what is the value of $$p+q+r?$$

×