document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=135792>Question 135792</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Aleksandra has a 4 meter by 5 meter rectangular carrot garden. She would like to add a stone path around the entire garden. She has 22 square meters of stone available. What is the widest that she can make the path? It gives a hint that says Write an equation for the area. I have no idea what formula to use for this problem. I believe I have the correct topic listed above. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99496 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=99496\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula is just the formula for the area of a rectangle, namely <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=LW ALIGN=MIDDLE  ALT=\"A=LW\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  The thing you have to deal with is that you actually have two rectangles, first is the 4m by 5m garden, and the second is the outside edge of the walkway around it.  Presuming that Alexsandra intends to build the walkway of uniform width all the way around, you can say that the width of the walkway is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >.   That means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > is added to the dimensions of the garden to get the dimensions of the outside edge of the walkway -- x on either side, x on the top, x on the bottom.  Next you have to realize that the actual surface area of the walkway is the area of the rectangle defined by the outer edge of the walkway MINUS the area of the garden.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C600%2C-1%2C8%2C-1%2C7%2C%0D%0Arectangle%280%2C0%2C7%2C6%29%2C%0D%0Arectangle%281%2C1%2C6%2C5%29%2C%0D%0Aline%28-.5%2C0%2C-.5%2C2.7%29%2C%0D%0Aline%28-.5%2C3.1%2C-.5%2C6%29%2C%0D%0Aline%28-.6%2C5.9%2C-.5%2C6%29%2C%0D%0Aline%28-.4%2C5.9%2C-.5%2C6%29%2C%0D%0Aline%28-.6%2C.1%2C-.5%2C0%29%2C%0D%0Aline%28-.4%2C.1%2C-.5%2C0%29%2C%0D%0Aline%280%2C-.6%2C3.2%2C-.6%29%2C%0D%0Aline%283.9%2C-.6%2C7%2C-.6%29%2C%0D%0Aline%280%2C-.6%2C.1%2C-.5%29%2C%0D%0Aline%280%2C-.6%2C.1%2C-.7%29%2C%0D%0Aline%286.9%2C-.5%2C7%2C-.6%29%2C%0D%0Aline%286.9%2C-.7%2C7%2C-.6%29%2C%0D%0Alocate%28.5%2C3%2Cx%29%2C%0D%0Alocate%281.5%2C3%2C4%29%2C%0D%0Alocate%28-.8%2C3%2C4%2B2x%29%0D%0Alocate%286.5%2C3%2Cx%29%2C%0D%0Alocate%283.5%2C.5%2Cx%29%2C%0D%0Alocate%283.5%2C1.5%2C5%29%2C%0D%0Alocate%283.3%2C-.5%2C5%2B2x%29%2C%0D%0Alocate%283.5%2C5.5%2Cx%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Area of the garden <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4%2A5=20 ALIGN=MIDDLE  ALT=\"A=4%2A5=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Area of the rectangle defined by the outer edge of the walkway <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%282x%2B4%29%282x%2B5%29=4x%5E2%2B18x%2B20 ALIGN=MIDDLE  ALT=\"A=%282x%2B4%29%282x%2B5%29=4x%5E2%2B18x%2B20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Area of outer rectangle MINUS Area of garden <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4x%5E2%2B18x ALIGN=MIDDLE  ALT=\"A=4x%5E2%2B18x\"   DISABLED_style= \"max-width:90%; height:auto;\" >  and this area must be equal to 22 square meters because that is the amount of walkway material available.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B18x=22 ALIGN=MIDDLE  ALT=\"4x%5E2%2B18x=22\"   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%2B18x-22=0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B18x-22=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, in standard form\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B9x-11=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B9x-11=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after dividing by 2 to eliminate a common factor\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%2B11%29%28x-1%29=0 ALIGN=MIDDLE  ALT=\"%282x%2B11%29%28x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after factoring\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B11=0 ALIGN=MIDDLE  ALT=\"2x%2B11=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1=0 ALIGN=MIDDLE  ALT=\"x-1=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=x=-%282%2F11%29 ALIGN=MIDDLE  ALT=\"x=-%282%2F11%29\"   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;\" >.  The negative root makes no sense when we are looking for a measure of length, so exclude that root as extraneous.  Therefore, <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;\" > meaning the walkway is 1 meter wide.\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "If the walkway is 1 meter wide, then the outside dimensions of the walkway must be (4 + 2 = 6) and (5 + 2 = 7).  6 * 7 = 42, less the area of the actual garden, 20, leaves 22 square meters of area for the walkway. </SPAN>\n" );
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