Find the rectangle in the ellipse with the smallest perimeter.
I know that if then .
However in the solutions it says that . Why isnt this for the perimeter of the rectangle? Or is this a mistake in the solution? :/
4x+4y is the perimeter of the rectangle.
Think for a moment, the ellipse is one which is clearly centered at the origin.
Hence, the length and breath of the rectangle would have to span both the -ve/+ve x and y axes in a symmetrical fashion to sit snugly within the ellipse.
The horizontal side of the rectangle would be 2x.
The vertical side of the rectangle would be 2y.
Hence, perimeter would be 2* (2x+2y)= 4x+4y
Hope this helps. Peace.
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