# Tricky Triplet Trepidation

Algebra Level 3

Let $$(a, b, c)$$ be an ordered triplet of positive real numbers such that

$\dfrac{3a + 8b + 36c}{\sqrt{a^2 + 4b^2 + 9c^2}} = 13.$

The sum of all possible values of $$\dfrac{a + b}{c}$$ can be written in the form $$\dfrac{p}{q},$$ where $$p$$ and $$q$$ are positive coprime integers. Find the value of $$p + q.$$

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