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A given right triangle has a hypotenuse of length $4$.

If one of the angles is double the size of another angle, in which range are all possible areas of this triangle contained?

$ \sqrt3 \leq A \leq 2\sqrt3 $

$ \cfrac{2}{\sqrt3} \leq A \leq \cfrac{4}{\sqrt3} $

$ 4\sqrt3 \leq A \leq \cfrac{8}{\sqrt3} $

$ 2 \leq A \leq 4 $

None of these ranges contains all the possible areas.