document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120170>Question 120170</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a factoring word problem when you have to use the principle of zero. The problem says A garden that is 4 meters wide and 6 meters long is to have a uniform border such that the area of the border is the same as the area of the garden. Find the width of the border. Could you please help me? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88055 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=88055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First let's draw a picture. We can see that the length of the large rectangle is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2B2x ALIGN=MIDDLE  ALT=\"6%2B2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the width of the large rectangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B2x ALIGN=MIDDLE  ALT=\"4%2B2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > since we are adding <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both the length and the width. note: the inner blue rectangle is the garden\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-10%2C7%2C-7%2C7%2C%0D%0Ablue%28line%28-5%2C3%2C5%2C3%29%29%2C%0D%0Ablue%28line%285%2C3%2C5%2C-3%29%29%2C%0D%0Ablue%28line%285%2C-3%2C-5%2C-3%29%29%2C%0D%0Ablue%28line%28-5%2C-3%2C-5%2C3%29%29%2C%0D%0Ared%28line%28-6%2C4%2C6%2C4%29%29%2C%0D%0Ared%28line%286%2C4%2C6%2C-4%29%29%2C%0D%0Ared%28line%286%2C-4%2C-6%2C-4%29%29%2C%0D%0Ared%28line%28-6%2C-4%2C-6%2C4%29%29%2C%0D%0Agreen%28line%28-5%2C3%2C-5%2C4%29%29%2C%0D%0Agreen%28line%28-5%2C3%2C-6%2C3%29%29%2C%0D%0Agreen%28line%285%2C3%2C5%2C4%29%29%2C%0D%0Agreen%28line%285%2C3%2C6%2C3%29%29%2C%0D%0Agreen%28line%28-5%2C-3%2C-5%2C-4%29%29%2C%0D%0Agreen%28line%28-5%2C-3%2C-6%2C-3%29%29%2C%0D%0Agreen%28line%285%2C-3%2C6%2C-3%29%29%2C%0D%0Agreen%28line%285%2C-3%2C5%2C-4%29%29%2C%0D%0Ared%28locate%28-0.5%2C4.5%2CLength%3A6%2B2x%29%29%2C%0D%0Ablue%28locate%28-0.5%2C3.5%2CLength%3A6%29%29%2C%0D%0Ared%28locate%28-8.95%2C0%2CWidth%3A4%2B2x%29%29%2C%0D%0Ablue%28locate%28-7.05%2C1.2%2CWidth%3A4%29%29%2C%0D%0Agreen%28locate%28-4.8%2C3.8%2Cx%29%29%2C%0D%0Agreen%28locate%28-5.6%2C3%2Cx%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From the drawing, we can see that the area of the small rectangle is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=L%2AW=6%2A4=24 ALIGN=MIDDLE  ALT=\"A=L%2AW=6%2A4=24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also, from the drawing, the area of larger rectangle is:\r<BR>\n" );
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document.write( "Now since we only want the area of the walkway, just subtract the area of the garden from the larger rectangle's area to get \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%286%2B2x%29%284%2B2x%29-24 ALIGN=MIDDLE  ALT=\"A=%286%2B2x%29%284%2B2x%29-24\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now since the area of the walkway is the same as the garden, this means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=24 ALIGN=MIDDLE  ALT=\"A=24\"   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=24=%286%2B2x%29%284%2B2x%29-24 ALIGN=MIDDLE  ALT=\"24=%286%2B2x%29%284%2B2x%29-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=24 ALIGN=MIDDLE  ALT=\"A=24\"   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=24=4x%5E2%2B20x%2B24-24 ALIGN=MIDDLE  ALT=\"24=4x%5E2%2B20x%2B24-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=4x%5E2%2B20x%2B24-24-24 ALIGN=MIDDLE  ALT=\"0=4x%5E2%2B20x%2B24-24-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 24 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=4x%5E2%2B20x-24 ALIGN=MIDDLE  ALT=\"0=4x%5E2%2B20x-24\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28x%2B6%29%28x-1%29=0 ALIGN=MIDDLE  ALT=\"4%28x%2B6%29%28x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the right side \r<BR>\n" );
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document.write( "Now set each factor equal to zero:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >    Now solve for x in each case\r<BR>\n" );
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document.write( "So our possible answers are \r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "However, since a negative length doesn't make sense, our only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So the walkway's width is 1 meter </SPAN>\n" );
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