document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=712636>Question 712636</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having trouble with this one! A rectangular garden has dimensions 3m by 4m. A path is built around the garden. The area of the garden and path is 6 times as great as the area of the garden. What is the width of the path? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #438083 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=438083\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The area of the garden is 3*4 = 12 square meters.\r<BR>\n" );
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document.write( "Multiply this by 6 to get 12*6 = 72. We do this because \"The area of the garden and path is 6 times as great as the area of the garden\"\r<BR>\n" );
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document.write( "So the area of the garden+path = 72 square meters\r<BR>\n" );
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document.write( "So if x = width of the path, then the width goes from 3 to 3+2x meters. This is because you're adding x to each direction on the width. Similarly, the length jumps from 4 to 4+2x meters\r<BR>\n" );
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document.write( "The area of the garden+path in algebraic form is\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2B2x%29%284%2B2x%29 ALIGN=MIDDLE  ALT=\"%283%2B2x%29%284%2B2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "but this is 72 square meters which is what we found earlier, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2B2x%29%284%2B2x%29+=+72 ALIGN=MIDDLE  ALT=\"%283%2B2x%29%284%2B2x%29+=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12+%2B+6x+%2B+8x+%2B+4x%5E2+=+72 ALIGN=MIDDLE  ALT=\"12+%2B+6x+%2B+8x+%2B+4x%5E2+=+72\"   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=12+%2B+6x+%2B+8x+%2B+4x%5E2+-+72+=+0 ALIGN=MIDDLE  ALT=\"12+%2B+6x+%2B+8x+%2B+4x%5E2+-+72+=+0\"   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=4x%5E2+%2B+14x+-+60+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2+%2B+14x+-+60+=+0\"   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=2%282x%5E2+%2B+7x+-+30%29+=+0 ALIGN=MIDDLE  ALT=\"2%282x%5E2+%2B+7x+-+30%29+=+0\"   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=2x%5E2+%2B+7x+-+30+=+0%2F2 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+7x+-+30+=+0%2F2\"   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=2x%5E2+%2B+7x+-+30+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+7x+-+30+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now use the quadratic formula to solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%287%29%2B-sqrt%28%287%29%5E2-4%282%29%28-30%29%29%29%2F%282%282%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%287%29%2B-sqrt%28%287%29%5E2-4%282%29%28-30%29%29%29%2F%282%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+2 ALIGN=MIDDLE  ALT=\"a+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+7 ALIGN=MIDDLE  ALT=\"b+=+7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+-30 ALIGN=MIDDLE  ALT=\"c+=+-30\"   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+=+%28-7%2B-sqrt%2849-%28-240%29%29%29%2F%284%29 ALIGN=MIDDLE  ALT=\"x+=+%28-7%2B-sqrt%2849-%28-240%29%29%29%2F%284%29\"   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+=+%28-7%2B-sqrt%28289%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-7%2B-sqrt%28289%29%29%2F4\"   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+=+%28-7%2Bsqrt%28289%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-7%2Bsqrt%28289%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-7-sqrt%28289%29%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-7-sqrt%28289%29%29%2F4\"   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+=+%28-7%2B17%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-7%2B17%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-7-17%29%2F4 ALIGN=MIDDLE  ALT=\"x+=+%28-7-17%29%2F4\"   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+=+10%2F4 ALIGN=MIDDLE  ALT=\"x+=+10%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-24%2F4 ALIGN=MIDDLE  ALT=\"x+=+-24%2F4\"   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+=+5%2F2 ALIGN=MIDDLE  ALT=\"x+=+5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <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;\" >\r<BR>\n" );
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document.write( "Toss out the negative solution since a negative width of the path makes no sense at all.\r<BR>\n" );
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document.write( "So the only reasonable answer is 5/2 = 2.5 meters\r<BR>\n" );
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document.write( "Therefore, in the end, the width of the path is <font color=\"red\">2.5 meters</font> </SPAN>\n" );
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