document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209520>Question 1209520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (39) Square SQUR has sides of length x. If triangle SQE is equilateral, find the area of triangle QAU.<BR>\n" );
document.write( "Link to diagram: https://ibb.co/C58rZ09R </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851844 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=851844\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Tutor @ikleyn has provided a response showing a valid solution using equations of the lines in the figure.<br><BR>\n" );
document.write( "Here is a very different solution.<br><BR>\n" );
document.write( "Draw segment AP parallel to SQ with P on QU.  Let a be the length of AP.<br><BR>\n" );
document.write( "Angle PUA is 45 degrees, so triangle APU is a 45-45-90 right triangle.  The length of PU is then a.<br><BR>\n" );
document.write( "Angle SQA is 60 degrees, so angle AQP is 30 degrees; that make triangle APQ a 30-60-90 right triangle.  So then the length of QP is a*sqrt(3).<br><BR>\n" );
document.write( "Use the lengths of PU and QP to find an expression for a in terms of the side length of the square.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Ba%2Asqrt%283%29=x ALIGN=MIDDLE  ALT=\"a%2Ba%2Asqrt%283%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%281%2Bsqrt%283%29%29=x ALIGN=MIDDLE  ALT=\"a%281%2Bsqrt%283%29%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=x%2F%281%2Bsqrt%283%29%29 ALIGN=MIDDLE  ALT=\"a=x%2F%281%2Bsqrt%283%29%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=%28x%28sqrt%283%29-1%29%29%2F%28%28sqrt%283%29%2B1%29%28sqrt%283%29-1%29%29 ALIGN=MIDDLE  ALT=\"a=%28x%28sqrt%283%29-1%29%29%2F%28%28sqrt%283%29%2B1%29%28sqrt%283%29-1%29%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=%28x%2F2%29%28sqrt%283%29-1%29 ALIGN=MIDDLE  ALT=\"a=%28x%2F2%29%28sqrt%283%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Use the standard formula one-half base times height to find the area of triangle QAU.  The base is x and the height is a.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%281%2F2%29%28x%29%28%28x%2F2%29%28sqrt%283%29-1%29%29=%28x%5E2%2F4%29%28sqrt%283%29-1%29 ALIGN=MIDDLE  ALT=\"A=%281%2F2%29%28x%29%28%28x%2F2%29%28sqrt%283%29-1%29%29=%28x%5E2%2F4%29%28sqrt%283%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%2F4%29%28sqrt%283%29-1%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%2F4%29%28sqrt%283%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
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