document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=100153>Question 100153</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Geomatry. The length of a rectangle is 1 cm longer than its width. If the diagnonal of the rectangle is 4cm what are the dimensions (the length and teh width) of the rectangle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #72975 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=72975\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The statement that the \"length is 1 cm longer than the width\" means that we can define the length (l) = w + 1.  Width (w) is simply = to w. So, the rectangle has sides of w, w+1, w, and w+1.  The diagonal is known to be 4 cm (given).\r<BR>\n" );
document.write( "\n" );
document.write( "Now we simply apply the Pythagorean formula. Let's call the diagonal d.  That means \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2+=+w%5E2+%2B+%28w%2B1%29%5E2 ALIGN=MIDDLE  ALT=\"d%5E2+=+w%5E2+%2B+%28w%2B1%29%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=%28w%2B1%29%5E2+=+w%5E2+%2B+2w+%2B+1 ALIGN=MIDDLE  ALT=\"%28w%2B1%29%5E2+=+w%5E2+%2B+2w+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2+=+w%5E2+%2B+w%5E2+%2B+2w+%2B+1+=+2w%5E2+%2B+2w+%2B+1 ALIGN=MIDDLE  ALT=\"d%5E2+=+w%5E2+%2B+w%5E2+%2B+2w+%2B+1+=+2w%5E2+%2B+2w+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Of course, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2 ALIGN=MIDDLE  ALT=\"d%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the square of the diagonal, and we were told the diagonal was 4 cm, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%5E2+=+16 ALIGN=MIDDLE  ALT=\"d%5E2+=+16\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "\n" );
document.write( "Substituting what we know:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16+=+2w%5E2+%2B+2w+%2B+1 ALIGN=MIDDLE  ALT=\"16+=+2w%5E2+%2B+2w+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Subtracting 16 from both sides:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+2w%5E2+%2B+2w+-+15 ALIGN=MIDDLE  ALT=\"0+=+2w%5E2+%2B+2w+-+15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "This does not factor easily, so you can use the quadratic equation to find w.\r<BR>\n" );
document.write( "\n" );
document.write( "Quadratic formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Substituing, we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A2%2A%28-15%29+%29%29%2F%282%2A2%29+ ALIGN=MIDDLE  ALT=\"w+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A2%2A%28-15%29+%29%29%2F%282%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );