# An almost nonexistent Triangle

Geometry Level 3

Find the area of a triangle for which the side lengths, $$a, b$$ and $$c$$ are $$15, 11$$ and $$\dfrac{77}{3}$$, respectively.

If this area is of the form $$\dfrac{r}{s}\sqrt{kmn}$$, where $$r$$ and $$s$$ are relatively prime and $$k,m$$ and $$n$$ are distinct prime numbers, evaluate $$r+s+k+m+n.$$

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