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# Lagrange multipliers question help please :)

1. 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? :/

Thanks
2. 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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