# Find that length!

Geometry Level 5

There exists a triangle $$ABC$$ with $$AB=5$$ and $$AC=7$$. Let $$D$$ be a point on $$BC$$ such that $$CD=2BD$$. Given that $$\angle A$$ is obtuse, the area of $$\triangle ABC = \frac{21\sqrt{11}}{4}$$, and the length of $$AD$$ can be expressed in the form $$\sqrt{n}$$ where $$n$$ is an integer, find the value of $$n$$.

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