document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=28978>Question 28978</A>: <I><SPAN STYLE=\"word-break: break-all;\">  thanks for your help.  A garden area is 30 ft long and 20 ft wide.  A path of uniform width is set around the edge.  If the remaining garden area is 400ft^, what is the width of the path?<BR>\n" );
document.write( "A=(2)LW<BR>\n" );
document.write( "2x30.20=1200 \r<BR>\n" );
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document.write( "1200-400=800 sq ft left\r<BR>\n" );
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document.write( "could the path be 20 ft wide?   20 times 20 times 2=800<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15823 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=15823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It sounds like the path is constructed IN and not AROUND the garden, so<BR>\n" );
document.write( "it diminishes the amount of gardent area.<BR>\n" );
document.write( "Let the uniform width of the path be \"x\".<BR>\n" );
document.write( "If you draw the picture you will see that the remaining garden space is<BR>\n" );
document.write( "a rectangle with a width of 30-2x and a length of 20-2x.<BR>\n" );
document.write( "EQUATION:<BR>\n" );
document.write( "(30-2x)(20-2x)=400<BR>\n" );
document.write( "2(15-x)2(10-x)=400<BR>\n" );
document.write( "(15-x)(10-x)=100<BR>\n" );
document.write( "150-25x+x^2=100<BR>\n" );
document.write( "x^2-25x+50=0<BR>\n" );
document.write( "<TABLE  BORDER=1>\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-25x%2B50+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-25x%2B50+=+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=%28-25%29%5E2-4%2A1%2A50=425 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-25%29%5E2-4%2A1%2A50=425\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=425 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--25%2B-sqrt%28+425+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--25%2B-sqrt%28+425+%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-%28-25%29%2Bsqrt%28+425+%29%29%2F2%5C1+=+22.8077640640442 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-25%29%2Bsqrt%28+425+%29%29%2F2%5C1+=+22.8077640640442\"   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-%28-25%29-sqrt%28+425+%29%29%2F2%5C1+=+2.19223593595585 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-25%29-sqrt%28+425+%29%29%2F2%5C1+=+2.19223593595585\"   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-25x%2B50 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-25x%2B50\"   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-25x%2B50+=+1%28x-22.8077640640442%29%2A%28x-2.19223593595585%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-25x%2B50+=+1%28x-22.8077640640442%29%2A%28x-2.19223593595585%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 22.8077640640442, 2.19223593595585.\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-25%2Ax%2B50+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-25%2Ax%2B50+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Hope this helps<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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