Lagrange multipliers question help please :)
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Lagrange multipliers question help please :)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? :/
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Re: Lagrange multipliers question help please :)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.
