document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=503498>Question 503498</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a community flower garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 285 square meters. What ill be the width of the pathway?<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 #339268 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=339268\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Borders are interesting because you have to remember that you have to pave the 4 corners.<BR>\n" );
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document.write( "The area of the garden = 12*16 = 192 square meters.<BR>\n" );
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document.write( "Then you add the border with width 'x'.<BR>\n" );
document.write( "So,<BR>\n" );
document.write( "Length is now L + 2x<BR>\n" );
document.write( "Width is now W + 2x<BR>\n" );
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document.write( "We are told:<BR>\n" );
document.write( "(L+2x)(W+2x) = 285 <BR>\n" );
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document.write( "(12+2x)(16+2x) = 285<BR>\n" );
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document.write( "192 +24x +32x +4x^2 = 285<BR>\n" );
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document.write( "4x^2 + 56x + 192 = 285<BR>\n" );
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document.write( "4x^2 + 56x - 93 = 0<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=4x%5E2%2B56x%2B-93+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B56x%2B-93+=+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=%2856%29%5E2-4%2A4%2A-93=4624 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2856%29%5E2-4%2A4%2A-93=4624\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=4624 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+=+%28-56%2B-sqrt%28+4624+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-56%2B-sqrt%28+4624+%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-%2856%29%2Bsqrt%28+4624+%29%29%2F2%5C4+=+1.5 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2856%29%2Bsqrt%28+4624+%29%29%2F2%5C4+=+1.5\"   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-%2856%29-sqrt%28+4624+%29%29%2F2%5C4+=+-15.5 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2856%29-sqrt%28+4624+%29%29%2F2%5C4+=+-15.5\"   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=4x%5E2%2B56x%2B-93 ALIGN=MIDDLE  ALT=\"4x%5E2%2B56x%2B-93\"   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=4x%5E2%2B56x%2B-93+=+4%28x-1.5%29%2A%28x--15.5%29 ALIGN=MIDDLE  ALT=\"4x%5E2%2B56x%2B-93+=+4%28x-1.5%29%2A%28x--15.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.5, -15.5.\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+4%2Ax%5E2%2B56%2Ax%2B-93+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B56%2Ax%2B-93+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "You cannot have a negative width, so the border is 1.5 m.<BR>\n" );
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document.write( "Always check your work.<BR>\n" );
document.write( "L = 12 + 2(1.5) = 15<BR>\n" );
document.write( "W = 16 + 2(1.5) = 19<BR>\n" );
document.write( "15*19 = 285<BR>\n" );
document.write( "Correct.<BR>\n" );
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document.write( "Answer:  The border is 1.5 meters wide.<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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