My Math Forum optimization - rectangle in a semicircle

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 May 2nd, 2010, 04:54 AM #1 Newbie   Joined: May 2010 Posts: 1 Thanks: 0 optimization - rectangle in a semicircle A piece of plexiglass is in the shape of a semicircle with radius 2m. Determine the dimensions of the rectangle with the greatest area that can be cut from the piece of plexiglass. - I tried isolating y from x^2 + y^2 = 4 and substituting it in the formula for the area of the rectangle f(A) = 2xy. Then I found the derivative of f(A) and set it to zero, but I just can't seem to factor it correctly. Can anyone help me out? According to the textbook the answer is supposed to be 1.42m by 0.71m.
 May 2nd, 2010, 06:36 AM #2 Global Moderator     Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: optimization - rectangle in a semicircle It won't factor, at least with integers. Use the quadratic formula!
 May 2nd, 2010, 07:54 AM #3 Newbie   Joined: May 2010 Posts: 4 Thanks: 0 Re: optimization - rectangle in a semicircle Does the picture look something like that? If so just solve it by using 3triangles. y=(square root (r^2-x^2))*2

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### a piece of plexiglass is in the shape of a semicircle with radius 2m . determine the dimensions of the rectangle with the greatest area that can be cut from the piece of plexiglass

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