document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211995>Question 211995</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a farmer wants to set up a pigpen using 40 feet of fence to enclose a rectangular area of 51 square feet. what are the dimensions of the pigpen? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #160116 by </B><A HREF=/tutors/aboutme.mpl?userid=drj><B>drj(1380)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drj><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=drj><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=160116\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A farmer wants to set up a pigpen using 40 feet of fence to enclose a rectangular area of 51 square feet. what are the dimensions of the pigpen?\r<BR>\n" );
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document.write( "1.  Perimeter of a rectangle is 2x+2y=40 where x=one side of rectangle and y=the adjacent side of x.  We can simplify this as x+y=20 where we divided 2 on both sides of the equation.  That is,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B2y%29%2F2=40%2F2=20 ALIGN=MIDDLE  ALT=\"%282x%2B2y%29%2F2=40%2F2=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2By=20 ALIGN=MIDDLE  ALT=\"x%2By=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=20-x ALIGN=MIDDLE  ALT=\"y=20-x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2.  Area=xy=51 where area of rectangle is height times width.\r<BR>\n" );
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document.write( "3.   Substitute y in Step 1 into Step 2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xy=x%2820-x%29=51 ALIGN=MIDDLE  ALT=\"xy=x%2820-x%29=51\"   DISABLED_style= \"max-width:90%; height:auto;\" >  Multiplying the terms will yield:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x-x%5E2=51 ALIGN=MIDDLE  ALT=\"20x-x%5E2=51\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "4.  Put everything on the left side to the right.  That is, add -20x+x^2 from both sides of the equation to make the left side equal to zero.\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20x-x%5E2-20x%2Bx%5E2=+51%2Bx%5E2-20x ALIGN=MIDDLE  ALT=\"20x-x%5E2-20x%2Bx%5E2=+51%2Bx%5E2-20x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplifying will yield\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+51%2Bx%5E2-20x ALIGN=MIDDLE  ALT=\"0+=+51%2Bx%5E2-20x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Finally, the above equation is equivalent to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-20x%2B51=0 ALIGN=MIDDLE  ALT=\"x%5E2-20x%2B51=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "4.  Now this is just a Quadratic Equation so we can use the formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "where a=1, b=-20 and c=51\r<BR>\n" );
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document.write( "5.  Use the following steps to solve the quadratic equation.\r<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-20x%2B51+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-20x%2B51+=+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" );
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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" );
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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=%28-20%29%5E2-4%2A1%2A51=196 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-20%29%5E2-4%2A1%2A51=196\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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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--20%2B-sqrt%28+196+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--20%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=x%5B1%5D+=+%28-%28-20%29%2Bsqrt%28+196+%29%29%2F2%5C1+=+17 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-20%29%2Bsqrt%28+196+%29%29%2F2%5C1+=+17\"   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-%28-20%29-sqrt%28+196+%29%29%2F2%5C1+=+3 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-20%29-sqrt%28+196+%29%29%2F2%5C1+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-20x%2B51 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-20x%2B51\"   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-20x%2B51+=+1%28x-17%29%2A%28x-3%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-20x%2B51+=+1%28x-17%29%2A%28x-3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 17, 3.\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-20%2Ax%2B51+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-20%2Ax%2B51+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "6. The rectangular sides are 3 and 17.  As a check 3*17=51 (Area is 51 square feet) and Perimeter is 2*(3+17)=40 ft.  So everything checks out.\r<BR>\n" );
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document.write( "For Step-by-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.Tv/courses/IntroAlgebra </SPAN>\n" );
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