document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159731>Question 159731</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the dimensions of a rectangle whose perimeter is 26 meters and whose area is 40 square meters. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117769 by </B><A HREF=/tutors/aboutme.mpl?userid=KnightOwlTutor><B>KnightOwlTutor(293)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KnightOwlTutor><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=KnightOwlTutor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=117769\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We know that the perimeter is equal to the length of all the sides<BR>\n" );
document.write( "X=width<BR>\n" );
document.write( "Y=length\r<BR>\n" );
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document.write( "The perimeter of the rectangle=X+X+Y+Y=26\r<BR>\n" );
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document.write( "Simplify to 2X+2Y=26\r<BR>\n" );
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document.write( "we know that the area is the width multplied by the length<BR>\n" );
document.write( "XY=40<BR>\n" );
document.write( "We isolate X by dividing Y on both sides X=40/Y\r<BR>\n" );
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document.write( "Replace 40/Y for X in the perimeter equation\r<BR>\n" );
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document.write( "2(40/Y) +2Y=26\r<BR>\n" );
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document.write( "Multiply each term on both sides by Y\r<BR>\n" );
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document.write( "80+2Y^2=26Y\r<BR>\n" );
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document.write( "subtract 26Y from both sides\r<BR>\n" );
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document.write( "80-26Y+2Y^2=0\r<BR>\n" );
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document.write( "This is a quadratic equation <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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B-26x%2B80+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-26x%2B80+=+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=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%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=%28-26%29%5E2-4%2A2%2A80=36 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-26%29%5E2-4%2A2%2A80=36\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=36 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--26%2B-sqrt%28+36+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--26%2B-sqrt%28+36+%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=x%5B1%5D+=+%28-%28-26%29%2Bsqrt%28+36+%29%29%2F2%5C2+=+8 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-26%29%2Bsqrt%28+36+%29%29%2F2%5C2+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-26%29-sqrt%28+36+%29%29%2F2%5C2+=+5 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-26%29-sqrt%28+36+%29%29%2F2%5C2+=+5\"   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=2x%5E2%2B-26x%2B80 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-26x%2B80\"   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=2x%5E2%2B-26x%2B80+=+%28x-8%29%2A%28x-5%29 ALIGN=MIDDLE  ALT=\"2x%5E2%2B-26x%2B80+=+%28x-8%29%2A%28x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 8, 5.\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%2B-26%2Ax%2B80+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-26%2Ax%2B80+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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