document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=675817>Question 675817</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Norman Window is a rectangle with a semi-circle on top of it.  Big Sky Window is designing a Norman window that will require 8m of trim around the perimeter of the window.  What dimensions will allow the maximum amount of light to enter a house? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #420223 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=420223\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A Norman Window is a rectangle with a semi-circle on top of it.<BR>\n" );
document.write( "Big Sky Window is designing a Norman window that will require 8m of trim around the perimeter of the window.<BR>\n" );
document.write( "What dimensions will allow the maximum amount of light to enter a house?<BR>\n" );
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document.write( "This can be summed up in the statement:<BR>\n" );
document.write( "\"Find the max area for a perimeter of 8 meters\"<BR>\n" );
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document.write( "Let W = the width of the rectangular portion and the diameter of semi-circle <BR>\n" );
document.write( ".5W = the radius of the semicircle<BR>\n" );
document.write( "let L = the length of the rectangular portion (height of the window)<BR>\n" );
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document.write( "Perimeter<BR>\n" );
document.write( "2 vert lengths + 1 lower width + half the circumference<BR>\n" );
document.write( "2L + W + .5W*pi = 8<BR>\n" );
document.write( "2L + W + 1.57W = 8<BR>\n" );
document.write( "2L + 2.57W = 8<BR>\n" );
document.write( "Divide by 2<BR>\n" );
document.write( "L + 1.285W = 4<BR>\n" );
document.write( "L = (4-1.285W)<BR>\n" );
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document.write( "Area<BR>\n" );
document.write( "A = L*W + [.5*pi*(.5W)^2]<BR>\n" );
document.write( "A = L*W + [.5*pi*.25W^2<BR>\n" );
document.write( "A = L*W + .3927W^2<BR>\n" );
document.write( "Replace L with (4-1.285W)<BR>\n" );
document.write( "A = W(4-1.285W) + .3927W^2<BR>\n" );
document.write( "A = 4W-1.285W^2 + .3927W^2<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "A = -.8923W^2 + 4W<BR>\n" );
document.write( "Find the axis of symmetry<BR>\n" );
document.write( "W = -4/2(-.8923)<BR>\n" );
document.write( "W = -4/-1.7846<BR>\n" );
document.write( "W = 2.24 meters is the width of the window for max area<BR>\n" );
document.write( "Find L<BR>\n" );
document.write( "L = 4 - 1.285(2.24)<BR>\n" );
document.write( "L = 4 - 2.8784<BR>\n" );
document.write( "L = 1.12 meters is the height of the window for max area<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this by finding the perimeter<BR>\n" );
document.write( "p = 2(1.12 + 2.24 +(.5*pi*2.24)<BR>\n" );
document.write( "p = 2.24 + 2.24 + 3.52<BR>\n" );
document.write( "p = 8 meters  </SPAN>\n" );
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