document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=159212>Question 159212</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular patio is surrounded on three sides by a fence (the remaning side is up against the house). If the area of the patio is 38 meter square, and the total length of fence is 18 meters, what is the length and width of the patio. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #117354 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=117354\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The area of a rectangle is Length*Width<BR>\n" );
document.write( "In this example X=width Y=Length\r<BR>\n" );
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document.write( "We know that the area of the rectangle is- XY=38<BR>\n" );
document.write( "We know that the length of the fence that surrounds 3 sides =18<BR>\n" );
document.write( "The algebraic equation for this is X+Y+X=18=2X+Y=18\r<BR>\n" );
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document.write( "We alter the perimeter equation to isolate the Y variable<BR>\n" );
document.write( "2X+Y=18<BR>\n" );
document.write( "Subtract 2X from both sides<BR>\n" );
document.write( "Y=18-2X\r<BR>\n" );
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document.write( "Substitute 18-2X for Y in the area equation.\r<BR>\n" );
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document.write( "X(18-2X)=38\r<BR>\n" );
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document.write( "18X-2x^2=38\r<BR>\n" );
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document.write( "Rearrange terms to reflect a quadratic equation\r<BR>\n" );
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document.write( "-2x^2+18x-38=0\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=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%2B18x%2B-38+=+0 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B18x%2B-38+=+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" );
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=%2818%29%5E2-4%2A-2%2A-38=20 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2818%29%5E2-4%2A-2%2A-38=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=20 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+=+%28-18%2B-sqrt%28+20+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-18%2B-sqrt%28+20+%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-%2818%29%2Bsqrt%28+20+%29%29%2F2%5C-2+=+3.38196601125011 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2818%29%2Bsqrt%28+20+%29%29%2F2%5C-2+=+3.38196601125011\"   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-%2818%29-sqrt%28+20+%29%29%2F2%5C-2+=+5.61803398874989 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2818%29-sqrt%28+20+%29%29%2F2%5C-2+=+5.61803398874989\"   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%2B18x%2B-38 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B18x%2B-38\"   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%2B18x%2B-38+=+%28x-3.38196601125011%29%2A%28x-5.61803398874989%29 ALIGN=MIDDLE  ALT=\"-2x%5E2%2B18x%2B-38+=+%28x-3.38196601125011%29%2A%28x-5.61803398874989%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 3.38196601125011, 5.61803398874989.\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%2B18%2Ax%2B-38+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B18%2Ax%2B-38+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "There are two solutions to this problems X=5.6180 and X=3.381\r<BR>\n" );
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document.write( "If we use X value of 5.6180 we can plug to find out Y value Y=18-2X \r<BR>\n" );
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document.write( "Y is 6.764    (5.6180)(6.764)=38.000152\r<BR>\n" );
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document.write( "Length of the patio is 6.764 meters and the width of the patio is 5.6180 meters </SPAN>\n" );
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