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A geometry student wants to draw a triangle inscribed in the ellipse $x^2+4y^2=16$. What is the area of the largest rectangle that the student can draw?

I know the final solution is $16$, but I am not sure of how to get that answer.

N. F. Taussig
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    Triangle or rectangle? Please proof-read your question carefully before posting. – David Apr 08 '19 at 02:03
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