document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148073>Question 148073</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular field is fenced in by using a river as one side . If 2500 m<BR>\n" );
document.write( "of fencing are used for the 720,000-m2 field , what are its dimensions?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #108467 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=108467\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangular field is fenced in by using a river as one side . If 2500 m<BR>\n" );
document.write( "of fencing are used for the 720,000-m2 field , what are its dimensions? <BR>\n" );
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document.write( "Let L = length of rectangular field<BR>\n" );
document.write( "and W = width of rectangular field<BR>\n" );
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document.write( "Since we have two variables we'll need two equations.<BR>\n" );
document.write( "From the fact that there is 2500 m of fencing, we can get our first equation (perimeter):<BR>\n" );
document.write( "2W+L = 2500<BR>\n" );
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document.write( "From the given area (720000 sq meters) we can get our second equation (area):<BR>\n" );
document.write( "LW = 720000<BR>\n" );
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document.write( "Solving equation 1 for L we get:<BR>\n" );
document.write( "2W+L = 2500<BR>\n" );
document.write( "L = 2500-2W<BR>\n" );
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document.write( "Plug the above into equation 2 and solve for L:<BR>\n" );
document.write( "LW = 720000<BR>\n" );
document.write( "(2500-2W)W = 720000<BR>\n" );
document.write( "2500W-2W^2 = 720000<BR>\n" );
document.write( "0 = 2W^2 - 2500W + 720000<BR>\n" );
document.write( "dividing through by 2 we get:<BR>\n" );
document.write( "0 = W^2 - 1250W + 360000<BR>\n" );
document.write( "Using the quadratic equation we get two solutions for W:<BR>\n" );
document.write( "800m, 450m<BR>\n" );
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document.write( "If W=800m then<BR>\n" );
document.write( "2W+L = 2500<BR>\n" );
document.write( "2(800)+L = 2500<BR>\n" );
document.write( "1600+L = 2500<BR>\n" );
document.write( "L = 2500-1600<BR>\n" );
document.write( "L = 900<BR>\n" );
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document.write( "If W=450m then<BR>\n" );
document.write( "2W+L = 2500<BR>\n" );
document.write( "2(450)+L = 2500<BR>\n" );
document.write( "900+L = 2500<BR>\n" );
document.write( "L = 2500-900<BR>\n" );
document.write( "L = 1600<BR>\n" );
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document.write( "So, the dimensions of the field can be:<BR>\n" );
document.write( "900m by 800m<BR>\n" );
document.write( "or<BR>\n" );
document.write( "1600m by 450m<BR>\n" );
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document.write( "The quadratic solution follows:<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=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=1x%5E2%2B-1250x%2B360000+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-1250x%2B360000+=+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=%28-1250%29%5E2-4%2A1%2A360000=122500 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-1250%29%5E2-4%2A1%2A360000=122500\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=122500 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--1250%2B-sqrt%28+122500+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--1250%2B-sqrt%28+122500+%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-%28-1250%29%2Bsqrt%28+122500+%29%29%2F2%5C1+=+800 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-1250%29%2Bsqrt%28+122500+%29%29%2F2%5C1+=+800\"   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-%28-1250%29-sqrt%28+122500+%29%29%2F2%5C1+=+450 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-1250%29-sqrt%28+122500+%29%29%2F2%5C1+=+450\"   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=1x%5E2%2B-1250x%2B360000 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-1250x%2B360000\"   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=1x%5E2%2B-1250x%2B360000+=+1%28x-800%29%2A%28x-450%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-1250x%2B360000+=+1%28x-800%29%2A%28x-450%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 800, 450.\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+1%2Ax%5E2%2B-1250%2Ax%2B360000+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1250%2Ax%2B360000+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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