document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=73993>Question 73993</A>: <I><SPAN STYLE=\"word-break: break-all;\"> section 9.6 # 46\r<BR>\n" );
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document.write( "Geometry. The length of a rectangle is 1 cm longer than its width. If the diagonal of the rectangle is 5 cm, what are the dimensions (the length and 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 #53001 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=53001\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let L=length, w=width. <BR>\n" );
document.write( "The length and width can be represented as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=w%2B1 ALIGN=MIDDLE  ALT=\"L=w%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The diagonal of the rectangle is the hypotenuse of the triangle with legs of L and w. So the length and width can be found by Pythagoreans theorem.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L%29%5E2%2Bw%5E2=5%5E2 ALIGN=MIDDLE  ALT=\"%28L%29%5E2%2Bw%5E2=5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >Plug in w+1 into L<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w%2B1%29%5E2%2Bw%5E2=25 ALIGN=MIDDLE  ALT=\"%28w%2B1%29%5E2%2Bw%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >foil the (w+1)^2 term<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2%2B2w%2B2%2Bw%5E2=25 ALIGN=MIDDLE  ALT=\"w%5E2%2B2w%2B2%2Bw%5E2=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >Combine like terms and get everything to one side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2%2B2w-24=0 ALIGN=MIDDLE  ALT=\"2w%5E2%2B2w-24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plug this into the quadratic equation to solve for w<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=aw%5E2%2Bbw%2Bc=0 ALIGN=MIDDLE  ALT=\"aw%5E2%2Bbw%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2%2B2w%2B-24+=+0 ALIGN=MIDDLE  ALT=\"2w%5E2%2B2w%2B-24+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%282%29%5E2-4%2A2%2A-24=196 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%282%29%5E2-4%2A2%2A-24=196\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=196 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-2%2B-sqrt%28+196+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-2%2B-sqrt%28+196+%29%29%2F2%5Ca\"   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=w%5B1%5D+=+%28-%282%29%2Bsqrt%28+196+%29%29%2F2%5C2+=+3 ALIGN=MIDDLE  ALT=\"w%5B1%5D+=+%28-%282%29%2Bsqrt%28+196+%29%29%2F2%5C2+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5B2%5D+=+%28-%282%29-sqrt%28+196+%29%29%2F2%5C2+=+-4 ALIGN=MIDDLE  ALT=\"w%5B2%5D+=+%28-%282%29-sqrt%28+196+%29%29%2F2%5C2+=+-4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2%2B2w%2B-24 ALIGN=MIDDLE  ALT=\"2w%5E2%2B2w%2B-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2%2B2w%2B-24+=+2%28w-3%29%2A%28w--4%29 ALIGN=MIDDLE  ALT=\"2w%5E2%2B2w%2B-24+=+2%28w-3%29%2A%28w--4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 3, -4.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B2%2Ax%2B-24+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B2%2Ax%2B-24+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "This means the width is 3 (the negative width is ignored since it's not practical). So the length is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=w%2B1 ALIGN=MIDDLE  ALT=\"L=w%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=3%2B1 ALIGN=MIDDLE  ALT=\"L=3%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=4 ALIGN=MIDDLE  ALT=\"L=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the dimensions are: Width=3,Length=4<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2%2B4%5E2=5%5E2 ALIGN=MIDDLE  ALT=\"3%5E2%2B4%5E2=5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2B16=25 ALIGN=MIDDLE  ALT=\"9%2B16=25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25=25 ALIGN=MIDDLE  ALT=\"25=25\"   DISABLED_style= \"max-width:90%; height:auto;\" >Works </SPAN>\n" );
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