Optimization Question - Rectangle Inscribed in an Ellipse

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A rectangle is to be inscribed in the ellipse: 𝑥2/4 + 𝑦2 = 1
What should the dimensions of the rectangle be to maximise its area?
What is the maximum area?
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This video was great to check my Calc for a table build with an elliptical top. Thanks!

alexpatton
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That’s crazy I got the same answer, but with a different y value

micajahnordyke
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please dont chew gum while making videos, its not helping at all!! very provocating especially for people like me with adhd

sarah_bk