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Two triangles share a side as shown in the diagram. Triangle TUV is isosceles with side UV half the length of TV.

If triangle TSV is equilateral with area $16$, what is the length of UV?

$ 8\sqrt{3} $

$ 4\sqrt{3} $

$ \cfrac{8}{\sqrt{\sqrt{3}}} $

$ \cfrac{4}{\sqrt{\sqrt{3}}} $

$ \sqrt{3} $