# Minimum Value

Algebra Level 4

If $$x$$ and $$y$$ are real numbers such that $$5x+12y = 60$$ and the minimum value of $$\sqrt{x^2+y^2}$$ is equal to $$\dfrac ab$$ for coprime positive integers $$a$$ and $$b$$, find the value of $$a+b$$.

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