document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117871>Question 117871</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" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85938 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=85938\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If you create a diagonal in a rectangle, then you have created a right triangle with the diagonal as a hypotenuse.  Let's say the short leg of the triangle is x, and then the long leg (the long side of the rectangle) has to be x + 1.  And we are given that the hypotenuse is 4 cm.\r<BR>\n" );
document.write( "\n" );
document.write( "Pythagoras tells us that the sides and hypotenuse of a right triangle are related thus:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%2Bb%5E2=c%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%2Bb%5E2=c%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%5E2%2Bb%5E2%29=c ALIGN=MIDDLE  ALT=\"sqrt%28a%5E2%2Bb%5E2%29=c\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Replace a, b, and c with the values we are given:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%2B%28x%2B1%29%5E2%29=4 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%2B%28x%2B1%29%5E2%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Expand the binomial and combine terms under the radical\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%2Bx%5E2%2Bx%2Bx%2B1%29=4 ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%2Bx%5E2%2Bx%2Bx%2B1%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282x%5E2%2B2x%2B1%29=4 ALIGN=MIDDLE  ALT=\"sqrt%282x%5E2%2B2x%2B1%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Square both sides:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B2x%2B4=16 ALIGN=MIDDLE  ALT=\"2x%5E2%2B2x%2B4=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Add -16 to both sides:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B2x-15=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B2x-15=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use the quadratic formula\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A2%2A%28-15%29%29%29%2F%282%2A2%29+ ALIGN=MIDDLE  ALT=\"x+=+%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;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%28+124%29%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+124%29%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+2sqrt%28+31%29%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+2sqrt%28+31%29%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-1+%2B+sqrt%28+31%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-1+%2B+sqrt%28+31%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-1+-+sqrt%2831%29%29%2F2 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-1+-+sqrt%2831%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+%3C+0 ALIGN=MIDDLE  ALT=\"x%5B2%5D+%3C+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > so we can exclude this answer because we are looking for a positive number length.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2831%29%3E5 ALIGN=MIDDLE  ALT=\"sqrt%2831%29%3E5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D%3E0 ALIGN=MIDDLE  ALT=\"x%5B1%5D%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-1+%2B+sqrt%28+31%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-1+%2B+sqrt%28+31%29%29%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the answer we are seeking and is the width of the rectangle.  The length of the rectangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B1 ALIGN=MIDDLE  ALT=\"x%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the length must be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28-1+%2B+sqrt%28+31%29%29%2F2%29%2B1+=%281+%2B+sqrt%28+31%29%29%2F2%29 ALIGN=MIDDLE  ALT=\"%28%28-1+%2B+sqrt%28+31%29%29%2F2%29%2B1+=%281+%2B+sqrt%28+31%29%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Hope this helps,<BR>\n" );
document.write( "Happy Holidays,<BR>\n" );
document.write( "John\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );