document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=279110>Question 279110</A>: <I><SPAN STYLE=\"word-break: break-all;\"> PLEASE HELP!! <BR>\n" );
document.write( "Show that an equilateral triangle with area A has sides of length 2squarerootA/3^(1/4).   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #203032 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=203032\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the sides of the triangle be S.<BR>\n" );
document.write( "The area of a triangle is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%281%2F2%29BH ALIGN=MIDDLE  ALT=\"A=%281%2F2%29BH\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this case, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=S ALIGN=MIDDLE  ALT=\"B=S\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we need to find H.<BR>\n" );
document.write( "Draw it out.<BR>\n" );
document.write( "The distance from the top vertex to the middle of the base is the height, H.<BR>\n" );
document.write( "It forms a right triangle with one leg, H, the other leg, S/2, and the hypotenuse, S.<BR>\n" );
document.write( "Use the Pythagorean theorem to find H in terms of S.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E2=H%5E2%2B%28S%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"S%5E2=H%5E2%2B%28S%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5E2=S%5E2-%281%2F4%29S%5E2 ALIGN=MIDDLE  ALT=\"H%5E2=S%5E2-%281%2F4%29S%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5E2=%283%2F4%29S%5E2 ALIGN=MIDDLE  ALT=\"H%5E2=%283%2F4%29S%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H=%28sqrt%283%29%2F2%29S ALIGN=MIDDLE  ALT=\"H=%28sqrt%283%29%2F2%29S\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then from the area formula,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%281%2F2%29BH ALIGN=MIDDLE  ALT=\"A=%281%2F2%29BH\"   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%2F2%29%28S%29%28sqrt%283%29%2F2%29S ALIGN=MIDDLE  ALT=\"A=%281%2F2%29%28S%29%28sqrt%283%29%2F2%29S\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28sqrt%283%29%2F4%29S%5E2 ALIGN=MIDDLE  ALT=\"A=%28sqrt%283%29%2F4%29S%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then moving those terms around.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E2=4A%2Fsqrt%283%29 ALIGN=MIDDLE  ALT=\"S%5E2=4A%2Fsqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=%282%2Asqrt%28A%29%29%2F%283%5E%281%2F4%29%29 ALIGN=MIDDLE  ALT=\"S=%282%2Asqrt%28A%29%29%2F%283%5E%281%2F4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );