document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=373688>Question 373688</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. The goal is to find the area of the largest possible Norman window with a perimeter of 35 feet?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #266025 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=266025\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A Norman window has the shape of a semicircle atop a rectangle so that the<BR>\n" );
document.write( " diameter of the semicircle is equal to the width of the rectangle.<BR>\n" );
document.write( " The goal is to find the area of the largest possible Norman window with a<BR>\n" );
document.write( " perimeter of 35 feet? <BR>\n" );
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document.write( "Let x = the width and diameter of the window<BR>\n" );
document.write( "Let L = the rectangle portion length of the window<BR>\n" );
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document.write( "radius of the semicircle = .5x<BR>\n" );
document.write( "half circumference of the semi circle = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A.5x ALIGN=MIDDLE  ALT=\"pi%2A.5x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.5708x<BR>\n" );
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document.write( "Perimeter:<BR>\n" );
document.write( "1.5708x + x + 2L = 35<BR>\n" );
document.write( "2.5708x + 2L = 35<BR>\n" );
document.write( "2L = (35-2.5708x)<BR>\n" );
document.write( "L = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >(35-2.5708x)<BR>\n" );
document.write( "L = 17.5 - 1.2854x<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The area:<BR>\n" );
document.write( "A = x * L<BR>\n" );
document.write( "Replace L with (17.5-1.2854x)<BR>\n" );
document.write( "A = x(17.5-1.2854x)<BR>\n" );
document.write( "A = -1.2854x^2 - 17.5x<BR>\n" );
document.write( "Max area occurs at the axis of symmetry of this quadratic equation<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-17.5%29%2F%282%2A-1.2854%29 ALIGN=MIDDLE  ALT=\"%28-17.5%29%2F%282%2A-1.2854%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-17.5%29%2F%28-2.5708%29 ALIGN=MIDDLE  ALT=\"%28-17.5%29%2F%28-2.5708%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 6.8072 ft the width that gives max area<BR>\n" );
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document.write( "Find the area, replace x with 6.8072<BR>\n" );
document.write( "A = -1.2854(6.8072^2) + 17.5(6.8072)<BR>\n" );
document.write( "A = -1.2854(46.3382) + 17.5(6.8072)<BR>\n" );
document.write( "A = -59.556 + 119.126<BR>\n" );
document.write( "A = 59.57 sq/ft, max area for 35 ft perimeter<BR>\n" );
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