document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=10295>Question 10295</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This was under the conic section of my book but I am not sure if it is a review or if it is really a conic section problem.  It seems really simple but after I looked at it for a while I realized I didn't know what to do.\r<BR>\n" );
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document.write( "Find the dimentions of a rectangle that has the area of 10 and a dioganal length of 5.\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #5438 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=5438\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = width of the rectangle<BR>\n" );
document.write( "y = length of the rectangle<BR>\n" );
document.write( "5 = diagonal of the rectangle\r<BR>\n" );
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document.write( "By the Theorem of Pythagoras, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2+%2B+y%5E2+=+25 ALIGN=MIDDLE  ALT=\"+x%5E2+%2B+y%5E2+=+25\"   DISABLED_style= \"max-width:90%; height:auto;\" >  By the way, this equation would be the equation of a circle, which is probably why this problem is in your conic section section of the book!!\r<BR>\n" );
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document.write( "Solve for y:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2+=+25+-+x%5E2 ALIGN=MIDDLE  ALT=\"y%5E2+=+25+-+x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+sqrt%2825+-+x%5E2%29+ ALIGN=MIDDLE  ALT=\"y+=+sqrt%2825+-+x%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Area = xy = 10<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%2Asqrt%2825-+x%5E2%29+=+10 ALIGN=MIDDLE  ALT=\"+x%2Asqrt%2825-+x%5E2%29+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Square both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2A+%2825-x%5E2%29+=+100+ ALIGN=MIDDLE  ALT=\"x%5E2+%2A+%2825-x%5E2%29+=+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Set the equation equal to zero by taking everything to the right side of the equation, in order to get the x^4 to have a positive coefficient.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25x%5E2+-+x%5E4+=+100+ ALIGN=MIDDLE  ALT=\"25x%5E2+-+x%5E4+=+100+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+x%5E4+-+25x%5E2+%2B+100 ALIGN=MIDDLE  ALT=\"0+=+x%5E4+-+25x%5E2+%2B+100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It doesn't always happen, but it sure feels good when it does--that math comes out even!  This does indeed factor!!\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+%28x%5E2+-+20%29%28x%5E2+-+5%29+ ALIGN=MIDDLE  ALT=\"0+=+%28x%5E2+-+20%29%28x%5E2+-+5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+20 ALIGN=MIDDLE  ALT=\"x%5E2+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+0%2B-sqrt%2820%29 ALIGN=MIDDLE  ALT=\"x+=+0%2B-sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+2%2Asqrt%285%29+or+-2%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"x=+2%2Asqrt%285%29+or+-2%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+5 ALIGN=MIDDLE  ALT=\"x%5E2+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%285%29+or+-sqrt%285%29+ ALIGN=MIDDLE  ALT=\"x+=+sqrt%285%29+or+-sqrt%285%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "It turns out that if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+sqrt%285%29 ALIGN=MIDDLE  ALT=\"x+=+sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+2sqrt%285%29 ALIGN=MIDDLE  ALT=\"y+=+2sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2sqrt%285%29 ALIGN=MIDDLE  ALT=\"x=2sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=sqrt%285%29 ALIGN=MIDDLE  ALT=\"y+=sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  So there is actually only one solution.  The rectangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%285%29 ALIGN=MIDDLE  ALT=\"2sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  \r<BR>\n" );
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document.write( "R^2 at SCC </SPAN>\n" );
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