# Quadrilateral Side Lengths

Geometry Level 3

$$ABCD$$ is a quadrilateral with $$\angle ABC = 90^\circ$$, $$\angle ACD = 90^\circ$$, $$AC = 30$$, $$BC = 18$$ and $$AD = 50$$. If $$BD = a\sqrt{b}$$, what is the value of $$a + b$$?

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