document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1061957>Question 1061957</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A square of side length S and an equilateral triangle of side length S are placed inside a rectangle of<BR>\n" );
document.write( "length 2S and width S as shown. What fraction of the area of the rectangle remains uncovered?\r<BR>\n" );
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document.write( "Image is in the link: http://prntscr.com/dkzrut </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #676728 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=676728\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How high is the equilateral triangle?  <BR>\n" );
document.write( "Base is S and the length of the other two of its sides also S each.  Pythagorean Theorem formula will help; imagine cutting the triangle into two parts along the altitude.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E2=%28%281%2F2%29S%29%5E2%2Ba%5E2 ALIGN=MIDDLE  ALT=\"S%5E2=%28%281%2F2%29S%29%5E2%2Ba%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, using \"a\" for the altitude length.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=S%5E2-S%5E2%2F4 ALIGN=MIDDLE  ALT=\"a%5E2=S%5E2-S%5E2%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=4S%5E2%2F4-S%5E2%2F4 ALIGN=MIDDLE  ALT=\"a%5E2=4S%5E2%2F4-S%5E2%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2=3S%5E2%2F4 ALIGN=MIDDLE  ALT=\"a%5E2=3S%5E2%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28a=S%2Asqrt%283%29%2F2%29 ALIGN=MIDDLE  ALT=\"highlight_green%28a=S%2Asqrt%283%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Area of the whole rectangle:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%2A2S ALIGN=MIDDLE  ALT=\"S%2A2S\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%282S%5E2%29 ALIGN=MIDDLE  ALT=\"highlight%282S%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Fraction of the area which is uncovered:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28totalArea-coveredArea%29%2FtotalArea ALIGN=MIDDLE  ALT=\"%28totalArea-coveredArea%29%2FtotalArea\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282S%5E2-%28S%5E2%2B%281%2F2%29S%2Aa%29%29%2F%282S%5E2%29 ALIGN=MIDDLE  ALT=\"%282S%5E2-%28S%5E2%2B%281%2F2%29S%2Aa%29%29%2F%282S%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Substitute for a:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282S%5E2-%28S%5E2%2B%281%2F2%29S%28S%2F2%29sqrt%283%29%29%29%2F%282S%5E2%29 ALIGN=MIDDLE  ALT=\"%282S%5E2-%28S%5E2%2B%281%2F2%29S%28S%2F2%29sqrt%283%29%29%29%2F%282S%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The simplification algebra steps are not shown here, but final result should be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28%284-sqrt%283%29%29%2F8%29 ALIGN=MIDDLE  ALT=\"highlight%28%284-sqrt%283%29%29%2F8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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