document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=986224>Question 986224</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A square and an equilateral triangle have equal perimeters. The area of the triangle is 163 square centimeters. How long, in centimeters, is a diagonal of the square? Express your answer in simplest radical form. \r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #607030 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=607030\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Triangle, side length s.<BR>\n" );
document.write( "Altitude cuts triangle into two special 30 60 90 triangles.<BR>\n" );
document.write( "A, the area of The equilateral triangle,<BR>\n" );
document.write( "A/2, area of one of the special triangles.<BR>\n" );
document.write( "a, altitude of the triangle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2B%28s%2F2%29%5E2=s%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2B%28s%2F2%29%5E2=s%5E2\"   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=s%5E2-%28s%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"a%5E2=s%5E2-%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=a%5E2=s%5E2-%281%2F4%29s%5E2 ALIGN=MIDDLE  ALT=\"a%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=a%5E2=%283%2F4%29s%5E2 ALIGN=MIDDLE  ALT=\"a%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=a=%28s%2F2%29sqrt%283%29 ALIGN=MIDDLE  ALT=\"a=%28s%2F2%29sqrt%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=A=2%28%281%2F2%29%28a%2F2%29%28s%2F2%29sqrt%283%29%29 ALIGN=MIDDLE  ALT=\"A=2%28%281%2F2%29%28a%2F2%29%28s%2F2%29sqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, one-half base times height, twice<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2a%2As%2Asqrt%283%29%2F%282%2A2%2A2%29 ALIGN=MIDDLE  ALT=\"A=2a%2As%2Asqrt%283%29%2F%282%2A2%2A2%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=a%2As%2Asqrt%283%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"A=a%2As%2Asqrt%283%29%2F%282%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substitute for a,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28%28s%2F2%29sqrt%283%29%29%2As%2Asqrt%283%29%2F%282%2A2%29 ALIGN=MIDDLE  ALT=\"A=%28%28s%2F2%29sqrt%283%29%29%2As%2Asqrt%283%29%2F%282%2A2%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=%283%2As%5E2%29%2F8 ALIGN=MIDDLE  ALT=\"A=%283%2As%5E2%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for s<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5E2=A%2A8%2F3 ALIGN=MIDDLE  ALT=\"s%5E2=A%2A8%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=2sqrt%282A%2F3%29 ALIGN=MIDDLE  ALT=\"s=2sqrt%282A%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The SQUARE<BR>\n" );
document.write( "Let x be the edge of square shape.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=3s ALIGN=MIDDLE  ALT=\"4x=3s\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "because perimeter of square is given as equal to perimeter of the equilateral triangle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%283%2F4%29s ALIGN=MIDDLE  ALT=\"x=%283%2F4%29s\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The diagonal of the square is d.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx%5E2=d%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%5E2=d%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=sqrt%282x%5E2%29 ALIGN=MIDDLE  ALT=\"d=sqrt%282x%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=x%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"d=x%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-<BR>\n" );
document.write( "Substitute for x to get better formula for d.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=%283%2F4%29s%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"d=%283%2F4%29s%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substitute for s to get yet a better formula for d.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=%283%2F4%29%2A%282sqrt%282A%2F3%29%29%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"d=%283%2F4%29%2A%282sqrt%282A%2F3%29%29%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=%283%2F2%29sqrt%282%29sqrt%282A%2F3%29 ALIGN=MIDDLE  ALT=\"d=%283%2F2%29sqrt%282%29sqrt%282A%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=%283%2F2%29sqrt%282%29sqrt%282%29sqrt%28A%2F3%29 ALIGN=MIDDLE  ALT=\"d=%283%2F2%29sqrt%282%29sqrt%282%29sqrt%28A%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=3%2Asqrt%28A%2F3%29 ALIGN=MIDDLE  ALT=\"d=3%2Asqrt%28A%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rationalize the expression, the denominator...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=3%2Asqrt%283%29sqrt%28A%29%2F3 ALIGN=MIDDLE  ALT=\"d=3%2Asqrt%283%29sqrt%28A%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and remember, given A=163....<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28d=sqrt%283%29sqrt%28163%29%29 ALIGN=MIDDLE  ALT=\"highlight%28d=sqrt%283%29sqrt%28163%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );