document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1104847>Question 1104847</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A window is in the shape of a rectangle surmounted by a semicircle. The height of the rectangle is 0.4m more than the width. The total area of the window is 10.4m2 find the width and height of the window. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #719546 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=719546\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the width of the rectangle  = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+ ALIGN=MIDDLE  ALT=\"+w+\"   DISABLED_style= \"max-width:90%; height:auto;\" > m<BR>\n" );
document.write( "The height of the rectangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+%2B+.4+ ALIGN=MIDDLE  ALT=\"+w+%2B+.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > m<BR>\n" );
document.write( "---------------------------------------<BR>\n" );
document.write( "The area of the semicircle = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F2%29%2Api%2A%28w%2F2%29%5E2+ ALIGN=MIDDLE  ALT=\"+%281%2F2%29%2Api%2A%28w%2F2%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > m2<BR>\n" );
document.write( "The total area is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w%2A%28+w+%2B+.4+%29+%2B+%281%2F2%29%2A%281%2F4%29%2Api%2Aw%5E2+=+10.4+ ALIGN=MIDDLE  ALT=\"+w%2A%28+w+%2B+.4+%29+%2B+%281%2F2%29%2A%281%2F4%29%2Api%2Aw%5E2+=+10.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > m2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w%5E2+%2B+.4w+%2B+%28+pi%2F8+%29%2Aw%5E2+=+10.4+ ALIGN=MIDDLE  ALT=\"+w%5E2+%2B+.4w+%2B+%28+pi%2F8+%29%2Aw%5E2+=+10.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > m2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28%28+pi+%2B+8+%29+%2F+8+%29%2Aw%5E2+%2B+.4w%5E2+-+10.4+=+0+ ALIGN=MIDDLE  ALT=\"+%28%28+pi+%2B+8+%29+%2F+8+%29%2Aw%5E2+%2B+.4w%5E2+-+10.4+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1.3927w%5E2+%2B+.4w+-+10.4+=+0+ ALIGN=MIDDLE  ALT=\"+1.3927w%5E2+%2B+.4w+-+10.4+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rounding off:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1.4w%5E2+%2B+.4w+-+10.4+=+0+ ALIGN=MIDDLE  ALT=\"+1.4w%5E2+%2B+.4w+-+10.4+=+0+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"+w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+1.4+ ALIGN=MIDDLE  ALT=\"+a+=+1.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+.4+ ALIGN=MIDDLE  ALT=\"+b+=+.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+c+=+-10.4+ ALIGN=MIDDLE  ALT=\"+c+=+-10.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+%28-.4+%2B-+sqrt%28+.4%5E2-4%2A1.4%2A%28-10.4%29+%29%29%2F%282%2A1.4%29+ ALIGN=MIDDLE  ALT=\"+w+=+%28-.4+%2B-+sqrt%28+.4%5E2-4%2A1.4%2A%28-10.4%29+%29%29%2F%282%2A1.4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+%28-.4+%2B-+sqrt%28+.16+%2B+58.24+%29%29%2F+2.8+ ALIGN=MIDDLE  ALT=\"+w+=+%28-.4+%2B-+sqrt%28+.16+%2B+58.24+%29%29%2F+2.8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+%28+-.4+%2B+sqrt%28+58.4+%29%29+%2F+2.8+ ALIGN=MIDDLE  ALT=\"+w+=+%28+-.4+%2B+sqrt%28+58.4+%29%29+%2F+2.8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+%28+-.4+%2B+7.642+%29+%2F+2.8+ ALIGN=MIDDLE  ALT=\"+w+=+%28+-.4+%2B+7.642+%29+%2F+2.8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+7.242+%2F+2.8+ ALIGN=MIDDLE  ALT=\"+w+=+7.242+%2F+2.8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+=+2.586+ ALIGN=MIDDLE  ALT=\"+w+=+2.586+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+w+%2B+.4+=+2.986+ ALIGN=MIDDLE  ALT=\"+w+%2B+.4+=+2.986+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "The height, including semicircle is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2.986+%2B+w%2F2+ ALIGN=MIDDLE  ALT=\"+2.986+%2B+w%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2.986+%2B+2.586%2F2+ ALIGN=MIDDLE  ALT=\"+2.986+%2B+2.586%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2.986+%2B+1.293=+4.279+ ALIGN=MIDDLE  ALT=\"+2.986+%2B+1.293=+4.279+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------------<BR>\n" );
document.write( "width = 2.586 m<BR>\n" );
document.write( "height = 4.279 m<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1.4w%5E2+%2B+.4w++=+10.4+ ALIGN=MIDDLE  ALT=\"+1.4w%5E2+%2B+.4w++=+10.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1.4%2A2.586%5E2+%2B+.4%2A2.586+=+10.4+ ALIGN=MIDDLE  ALT=\"+1.4%2A2.586%5E2+%2B+.4%2A2.586+=+10.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1.4%2A6.687+%2B+1.0344+=+10.4+ ALIGN=MIDDLE  ALT=\"+1.4%2A6.687+%2B+1.0344+=+10.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9.3618+%2B++1.0344+=+10.4+ ALIGN=MIDDLE  ALT=\"+9.3618+%2B++1.0344+=+10.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10.3962+=+10.4+ ALIGN=MIDDLE  ALT=\"+10.3962+=+10.4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Looks close enough -error due to rounding off\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );