document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117900>Question 117900</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Geometry. The length of a rectangle is 1 cm longer than its width. If the diagonal<BR>\n" );
document.write( "of the rectangle is 4 cm, what are the dimensions (the length and the width) of the rectangle?<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 #85930 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=85930\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "If the length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" > of a rectangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+cm ALIGN=MIDDLE  ALT=\"1+cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > longer than its width <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W ALIGN=MIDDLE  ALT=\"W\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+W+%2B+1cm ALIGN=MIDDLE  ALT=\"L+=+W+%2B+1cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "	<BR>\n" );
document.write( "the diagonal <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d+=+4cm ALIGN=MIDDLE  ALT=\"d+=+4cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "since the diagonal cutting a rectangle into two right triangles, we will use Pythagoras Theorem to find what the length and the width are\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2+=+L%5E2+%2B+W%5E2 ALIGN=MIDDLE  ALT=\"d%5E2+=+L%5E2+%2B+W%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >….substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "	<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284cm%29%5E2+=+%28W+%2B+1cm%29+%5E2+%2B+W%5E2 ALIGN=MIDDLE  ALT=\"%284cm%29%5E2+=+%28W+%2B+1cm%29+%5E2+%2B+W%5E2\"   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=16cm%5E2+=+W%5E2+%2B+2Wcm+%2B+1cm%5E2%2B+W%5E2 ALIGN=MIDDLE  ALT=\"16cm%5E2+=+W%5E2+%2B+2Wcm+%2B+1cm%5E2%2B+W%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16cm%5E2+=+2W%5E2+%2B+2Wcm+%2B+1cm%5E2 ALIGN=MIDDLE  ALT=\"16cm%5E2+=+2W%5E2+%2B+2Wcm+%2B+1cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16cm%5E2+%96+%281cm%29%5E2=+2W%5E2+%2B+2Wcm+ ALIGN=MIDDLE  ALT=\"16cm%5E2+%96+%281cm%29%5E2=+2W%5E2+%2B+2Wcm+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15cm%5E2+=+2W%5E2+%2B+2Wcm+ ALIGN=MIDDLE  ALT=\"15cm%5E2+=+2W%5E2+%2B+2Wcm+\"   DISABLED_style= \"max-width:90%; height:auto;\" >	<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0=2W%5E2+%2B+2Wcm+%96+15cm%5E2+ ALIGN=MIDDLE  ALT=\"+0=2W%5E2+%2B+2Wcm+%96+15cm%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >….now we can use quadratic formula to solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W ALIGN=MIDDLE  ALT=\"W\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2 ALIGN=MIDDLE  ALT=\"b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+-15 ALIGN=MIDDLE  ALT=\"c+=+-15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we will have:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5B1%2C2%5D=%28-2+%2B-+sqrt+%282%5E2+-4%2A2%2A%28-15%29+%29%29+%2F+%282%2A2%29 ALIGN=MIDDLE  ALT=\"W%5B1%2C2%5D=%28-2+%2B-+sqrt+%282%5E2+-4%2A2%2A%28-15%29+%29%29+%2F+%282%2A2%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=W%5B1%2C2%5D=%28-2+%2B-+sqrt+%284+%2B+120+%29%29+%2F+4 ALIGN=MIDDLE  ALT=\"W%5B1%2C2%5D=%28-2+%2B-+sqrt+%284+%2B+120+%29%29+%2F+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5B1%2C2%5D=%28-2+%2B-+sqrt+%28124+%29%29+%2F+4 ALIGN=MIDDLE  ALT=\"W%5B1%2C2%5D=%28-2+%2B-+sqrt+%28124+%29%29+%2F+4\"   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=W%5B1%2C2%5D=%28-2+%2B-+11.14+%29+%2F+4 ALIGN=MIDDLE  ALT=\"W%5B1%2C2%5D=%28-2+%2B-+11.14+%29+%2F+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we are looking for width, we need only positive solution:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5B1%5D=%28-2+%2B+11.14+%29+%2F+4 ALIGN=MIDDLE  ALT=\"W%5B1%5D=%28-2+%2B+11.14+%29+%2F+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5B1%5D=%28+9.14+%29+%2F+4 ALIGN=MIDDLE  ALT=\"W%5B1%5D=%28+9.14+%29+%2F+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5B1%5D+=+%282.285%29cm ALIGN=MIDDLE  ALT=\"W%5B1%5D+=+%282.285%29cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "	<BR>\n" );
document.write( "Then\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+W+%2B+%281cm%29 ALIGN=MIDDLE  ALT=\"L+=+W+%2B+%281cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+%282.285%29cm+%2B+%281cm%29 ALIGN=MIDDLE  ALT=\"L+=+%282.285%29cm+%2B+%281cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+%283.285%29cm+ ALIGN=MIDDLE  ALT=\"L+=+%283.285%29cm+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2+=+L%5E2+%2B+W%5E2 ALIGN=MIDDLE  ALT=\"d%5E2+=+L%5E2+%2B+W%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >….\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=+sqrt%28L%5E2+%2B+W%5E2%29 ALIGN=MIDDLE  ALT=\"d=+sqrt%28L%5E2+%2B+W%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >….<BR>\n" );
document.write( "	<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+=+sqrt%28%283.285%29%5E2+%2B+%28%282.285%29%5E2%29%29 ALIGN=MIDDLE  ALT=\"4+=+sqrt%28%283.285%29%5E2+%2B+%28%282.285%29%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >….\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+=+sqrt%28+10.79+%2B+5.22%29 ALIGN=MIDDLE  ALT=\"4+=+sqrt%28+10.79+%2B+5.22%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >….\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+=+sqrt%28+16%29 ALIGN=MIDDLE  ALT=\"4+=+sqrt%28+16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >….\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4+=+4 ALIGN=MIDDLE  ALT=\"4+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >….\r<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );