document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=952212>Question 952212</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Marie made a rectangular pen for her dog using a side of the barn for one side and 26 m of fencing for the remaining 3 sides. If the area enclosed was 72 m squared, find the dimensions of the pen. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #581519 by </B><A HREF=/tutors/aboutme.mpl?userid=macston><B>macston(5194)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=macston><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=macston><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=581519\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x=length perpendicular to wall; y=length parallel to wall<BR>\n" );
document.write( "2x+y=26m<BR>\n" );
document.write( "y=26m-2x<BR>\n" );
document.write( "x*y=72sq m<BR>\n" );
document.write( "x(26m-2x)=72sq m<BR>\n" );
document.write( "-2x^2+26x=72 sq m<BR>\n" );
document.write( "-2x^2+26x-72=0<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=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%2B26x%2B-72+=+0 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B26x%2B-72+=+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=%2826%29%5E2-4%2A-2%2A-72=100 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2826%29%5E2-4%2A-2%2A-72=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=100 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+100+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-26%2B-sqrt%28+100+%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-%2826%29%2Bsqrt%28+100+%29%29%2F2%5C-2+=+4 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2826%29%2Bsqrt%28+100+%29%29%2F2%5C-2+=+4\"   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-%2826%29-sqrt%28+100+%29%29%2F2%5C-2+=+9 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2826%29-sqrt%28+100+%29%29%2F2%5C-2+=+9\"   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%2B26x%2B-72 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B26x%2B-72\"   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%2B26x%2B-72+=+-2%28x-4%29%2A%28x-9%29 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B26x%2B-72+=+-2%28x-4%29%2A%28x-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 4, 9.\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%2B26%2Ax%2B-72+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B26%2Ax%2B-72+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
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document.write( "ANSWERS: x=4 m or x=9m<BR>\n" );
document.write( "For x=4 m:<BR>\n" );
document.write( "y=26m-2x=26m-8m=18m For x=4m, y=18m<BR>\n" );
document.write( "For x=9 m:<BR>\n" );
document.write( "y=26m-2x=26m-18m=8m For x=9m, y=8m<BR>\n" );
document.write( "CHECK<BR>\n" );
document.write( "(4m,18m):<BR>\n" );
document.write( "A=x*y<BR>\n" );
document.write( "72 sq m=4m*18m<BR>\n" );
document.write( "72 sq m=72 sq m<BR>\n" );
document.write( "(9m,8m)<BR>\n" );
document.write( "A=x*y<BR>\n" );
document.write( "72 sq m=8m*9m<BR>\n" );
document.write( "72 sq m=72 sq m </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );