document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189792>Question 1189792</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A square garden has a walkway 3 ft wide around its outer edge.If the area of the entire garden, including the walkway, is 18,000 ft^2, what are the<BR>\n" );
document.write( "dimensions of the planted area? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821258 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=821258\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "x = side length of the planted area (ie we ignore the walkway)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "When considering the walkway, we add on 3+3 = 6 feet for each dimension of the square.<BR>\n" );
document.write( "The x by x square bumps up to (x+6) by (x+6)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The larger square has area of <BR>\n" );
document.write( "(x+6)^2<BR>\n" );
document.write( "(x+6)*(x+6)<BR>\n" );
document.write( "x(x+6)+6(x+6)<BR>\n" );
document.write( "x^2+6x+6x+36<BR>\n" );
document.write( "x^2+12x+36\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Set this area expression equal to the desired area (18,000) and solve for x.<BR>\n" );
document.write( "x^2+12x+36 = 18,000<BR>\n" );
document.write( "x^2+12x+36-18,000 = 0<BR>\n" );
document.write( "x^2+12x-17,964 = 0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now turn to the quadratic formula<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%2812%29%2B-sqrt%28%2812%29%5E2-4%281%29%28-17964%29%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%2812%29%2B-sqrt%28%2812%29%5E2-4%281%29%28-17964%29%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-12%2B-sqrt%2872000%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12%2B-sqrt%2872000%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-12%2B-268.3281573%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12%2B-268.3281573%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-12%2B268.3281573%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12%2B268.3281573%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-12-268.3281573%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-12-268.3281573%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28256.3281573%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28256.3281573%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-280.32815728%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-280.32815728%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+128.16407865 ALIGN=MIDDLE  ALT=\"x+=+128.16407865\"   DISABLED_style= \"max-width:90%; height:auto;\" > or  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-140.16407863 ALIGN=MIDDLE  ALT=\"x+=+-140.16407863\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We ignore the negative x value because we cannot have negative side lengths.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The square planted area is roughly 128.16 feet by 128.16 feet.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Here's another way to solve.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We start off with some smaller square representing the plants only. Adding on the walkway of uniform with around all the edges will get us some larger square.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's say this larger square has side lengths of W. So W^2 is the area of this larger square.<BR>\n" );
document.write( "Set it equal to the 18,000 figure and solve for W\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W%5E2+=+18000 ALIGN=MIDDLE  ALT=\"W%5E2+=+18000\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+sqrt%2818000%29 ALIGN=MIDDLE  ALT=\"W+=+sqrt%2818000%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+134.164079 ALIGN=MIDDLE  ALT=\"W+=+134.164079\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The side lengths of the larger square are roughly 134.164079 feet\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We then subtract off 6 feet due to the 3+3 = 6 figure calculated earlier<BR>\n" );
document.write( "134.164079 - 6 = 128.164079\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We get the same result of 128.16 as earlier.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Depending on your preferences, this option may be much easier compared to the last method.<BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );