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May 2nd, 2010, 04:54 AM  #1 
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: 3  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 
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^2x^2))*2 

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