document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=268829>Question 268829</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the norman window with the dimensions of a rectangle with a base of 6 feet is topped by a semicircle. if the area of the window is 68.2 square feet, find the height h to the nearest tenth of a foot.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #196970 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=196970\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> (NOTE: A solution provided by another tutor fails to include the semicircle in the area of the window.)<br><BR>\n" );
document.write( "The area of the window = the area of the rectangle + the area of semicircle on top.<BR>\n" );
document.write( "The area of the rectangle is length times width. The width is 6 and we'll let x = the length. So the area of the rectangle is 6x.<br><BR>\n" );
document.write( "The area of a circle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The area of a semicircle would be half of this: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"%281%2F2%29pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since the radius of this semicircle is 3, the area of this semicircle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29pi%2A%283%29%5E2+=+%281%2F2%29pi%2A9+=+%289%2F2%29pi ALIGN=MIDDLE  ALT=\"%281%2F2%29pi%2A%283%29%5E2+=+%281%2F2%29pi%2A9+=+%289%2F2%29pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the total area of the window is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x+%2B+%289%2F2%29pi ALIGN=MIDDLE  ALT=\"6x+%2B+%289%2F2%29pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >. And we are told that this area is 68.2. So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=68.2+=+6x+%2B+%289%2F2%29pi ALIGN=MIDDLE  ALT=\"68.2+=+6x+%2B+%289%2F2%29pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we solve for x. Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2F2%29pi ALIGN=MIDDLE  ALT=\"%289%2F2%29pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > from each side:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=68.2+-+%289%2F2%29pi+=+6x ALIGN=MIDDLE  ALT=\"68.2+-+%289%2F2%29pi+=+6x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And divide both sides by 6:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2868.2+-+%289%2F2%29pi%29%2F6+=+x ALIGN=MIDDLE  ALT=\"%2868.2+-+%289%2F2%29pi%29%2F6+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the exact answer. We need a decimal approximation so we will use our calculators:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2868.2+-+14.1371669411540690%29%2F6+=+x ALIGN=MIDDLE  ALT=\"%2868.2+-+14.1371669411540690%29%2F6+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54.0628330588459310%2F6+=+x ALIGN=MIDDLE  ALT=\"54.0628330588459310%2F6+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9.0104721764743218+=+x ALIGN=MIDDLE  ALT=\"9.0104721764743218+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rounded to the nearest tenth of a foot, x = 9.0. x is the height of the rectangle. To get the total height (which is what the problem is asking you to find, I think) you will add the height of the semicircle to this giving 12.0 as an answer. </SPAN>\n" );
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