document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=857594>Question 857594</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I've spent so much time on this one problem and still can't figure it out! If you could help me out, it would be really appreciated!\r<BR>\n" );
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document.write( "A rectangle has a diagonal 20 inches long that forms angles of<BR>\n" );
document.write( "60° and 30° with the sides. Find the perimeter of the rectangle.\r<BR>\n" );
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document.write( "Thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #516666 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=516666\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The diagonal splits the rectangle into 2<BR>\n" );
document.write( "30-60-90 triangles. What you need to know<BR>\n" );
document.write( "for this problem is the proportions of the sides.<BR>\n" );
document.write( "(1) side opposite 30 degree angle: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+ ALIGN=MIDDLE  ALT=\"+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) side opposite 60 degree angle: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%283%29+ ALIGN=MIDDLE  ALT=\"+sqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(3) side opposite 90 degree angle: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2+ ALIGN=MIDDLE  ALT=\"+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( note that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1%5E2+%2B+sqrt%283%29%5E2+=+2%5E2+ ALIGN=MIDDLE  ALT=\"+1%5E2+%2B+sqrt%283%29%5E2+=+2%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > )<BR>\n" );
document.write( "---------------------------------------------<BR>\n" );
document.write( "Now you can say:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+%2F+20+=+1+%2F+2+ ALIGN=MIDDLE  ALT=\"+a+%2F+20+=+1+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( short side of given triangle ) / ( diagonal of given triangle ) =<BR>\n" );
document.write( "( ratio of short side / diagonal of all 30-60-90 triangles )<BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20+ ALIGN=MIDDLE  ALT=\"+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+10+ ALIGN=MIDDLE  ALT=\"+a+=+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "And also:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+%2F+20+=+sqrt%283%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+b+%2F+20+=+sqrt%283%29+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "( long side of given triangle ) / ( diagonal of given triangle ) =<BR>\n" );
document.write( "( ratio of long side / diagonal of all 30-60-90 triangles )<BR>\n" );
document.write( "Again, multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20+ ALIGN=MIDDLE  ALT=\"+20+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b+=+10%2Asqrt%283%29+ ALIGN=MIDDLE  ALT=\"+b+=+10%2Asqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "The perimeter, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P ALIGN=MIDDLE  ALT=\"P\"   DISABLED_style= \"max-width:90%; height:auto;\" >, is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+2a+%2B+2b+ ALIGN=MIDDLE  ALT=\"+P+=+2a+%2B+2b+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+P+=+2%2A10+%2B+2%2A10%2Asqrt%283%29+ ALIGN=MIDDLE  ALT=\"+P+=+2%2A10+%2B+2%2A10%2Asqrt%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=+P+=+20+%2B+20%2Asqrt%283%29+ ALIGN=MIDDLE  ALT=\"+P+=+20+%2B+20%2Asqrt%283%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Hope this isn't confusing<BR>\n" );
document.write( " </SPAN>\n" );
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