document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93440>Question 93440</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A garden area is 30ft. long and 20ft. wide. A path of uniform width is set around the edge. If the remaining garden is 400ft.^2, 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 #68030 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=68030\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If we draw a picture we get\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-5%2C5%2C-5%2C5%2C%0D%0Aline%28-5%2C5%2C5%2C5%29%2C%0D%0Aline%285%2C5%2C5%2C-5%29%2C%0D%0Aline%285%2C-5%2C-5%2C-5%29%2C%0D%0Aline%28-5%2C-5%2C-5%2C5%29%2C%0D%0A%0D%0Aarrow%28-3%2C3%2C-5%2C3%29%2C%0D%0Aarrow%28-5%2C3%2C-3%2C3%29%2C%0D%0Alocate%28-4%2C3%2Cx%29%2C%0D%0A%0D%0Aarrow%283%2C3%2C5%2C3%29%2C%0D%0Aarrow%285%2C3%2C3%2C3%29%2C%0D%0Alocate%284%2C3%2Cx%29%2C%0D%0A%0D%0A%0D%0Aarrow%283%2C3%2C3%2C5%29%2C%0D%0Aarrow%283%2C5%2C3%2C3%29%2C%0D%0Alocate%283%2C4%2Cx%29%2C%0D%0A%0D%0A%0D%0Aarrow%283%2C-3%2C3%2C-5%29%2C%0D%0Aarrow%283%2C-5%2C3%2C-3%29%2C%0D%0Alocate%283%2C-4%2Cx%29%2C%0D%0A%0D%0A%0D%0Alocate%280%2C3%2C30%29%2C%0D%0Alocate%283%2C0%2C20%29%2C%0D%0Arectangle%28-3%2C-3%2C3%2C3%29%0D%0A%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If we let x be the width of the path, notice there are 2 x-values per side. So we add 2x to 20 to get 20+2x. This is the total length of the side that contains 20 feet. \r<BR>\n" );
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document.write( "Also, this means we add 2x to 30 to get 30+2x. This is the total length of the side that contains 30 feet. \r<BR>\n" );
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document.write( "So that means the total area can be written as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%2820%2B2x%29%2830%2B2x%29 ALIGN=MIDDLE  ALT=\"A=%2820%2B2x%29%2830%2B2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now lets find the inner area:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=20%2A30=600 ALIGN=MIDDLE  ALT=\"A=20%2A30=600\"   DISABLED_style= \"max-width:90%; height:auto;\" > plug in the garden dimensions\r<BR>\n" );
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document.write( "So the inner area is 600 sq ft\r<BR>\n" );
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document.write( "Now lets find the total area\r<BR>\n" );
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document.write( "inner area+remaining area=600+400=1000\r<BR>\n" );
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document.write( "So the total area is 1000 sq ft\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000=%2820%2B2x%29%2830%2B2x%29 ALIGN=MIDDLE  ALT=\"1000=%2820%2B2x%29%2830%2B2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=1000 ALIGN=MIDDLE  ALT=\"A=1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > (this is the total area)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000=600%2B100x%2B4x%5E2 ALIGN=MIDDLE  ALT=\"1000=600%2B100x%2B4x%5E2\"   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=600%2B100x%2B4x%5E2-1000 ALIGN=MIDDLE  ALT=\"0=600%2B100x%2B4x%5E2-1000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 1000 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%2B100x-400 ALIGN=MIDDLE  ALT=\"0=4x%5E2%2B100x-400\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for x:\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<BR>\n" );
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document.write( "<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;\" >\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax%5E2%2B100%2Ax-400=0 ALIGN=MIDDLE  ALT=\"4%2Ax%5E2%2B100%2Ax-400=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4 ALIGN=MIDDLE  ALT=\"a=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=100 ALIGN=MIDDLE  ALT=\"b=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-400 ALIGN=MIDDLE  ALT=\"c=-400\"   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+=+%28-100+%2B-+sqrt%28+%28100%29%5E2-4%2A4%2A-400+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-100+%2B-+sqrt%28+%28100%29%5E2-4%2A4%2A-400+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=4, b=100, and c=-400\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-100+%2B-+sqrt%28+10000-4%2A4%2A-400+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-100+%2B-+sqrt%28+10000-4%2A4%2A-400+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 100 to get 10000  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-100+%2B-+sqrt%28+10000%2B6400+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-100+%2B-+sqrt%28+10000%2B6400+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-400%2A4 ALIGN=MIDDLE  ALT=\"-4%2A-400%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6400 ALIGN=MIDDLE  ALT=\"6400\"   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+=+%28-100+%2B-+sqrt%28+16400+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-100+%2B-+sqrt%28+16400+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-100+%2B-+20%2Asqrt%2841%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%28-100+%2B-+20%2Asqrt%2841%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-100+%2B-+20%2Asqrt%2841%29%29%2F8 ALIGN=MIDDLE  ALT=\"x+=+%28-100+%2B-+20%2Asqrt%2841%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 4 to get 8\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-100+%2B+20%2Asqrt%2841%29%29%2F8 ALIGN=MIDDLE  ALT=\"x+=+%28-100+%2B+20%2Asqrt%2841%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-100+-+20%2Asqrt%2841%29%29%2F8 ALIGN=MIDDLE  ALT=\"x+=+%28-100+-+20%2Asqrt%2841%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-100%2F8%2B20%2Asqrt%2841%29%2F8 ALIGN=MIDDLE  ALT=\"x=-100%2F8%2B20%2Asqrt%2841%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-100%2F8-20%2Asqrt%2841%29%2F8 ALIGN=MIDDLE  ALT=\"x=-100%2F8-20%2Asqrt%2841%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-25+%2F+2%2B5%2Asqrt%2841%29%2F2 ALIGN=MIDDLE  ALT=\"x=-25+%2F+2%2B5%2Asqrt%2841%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-25+%2F+2-5%2Asqrt%2841%29%2F2 ALIGN=MIDDLE  ALT=\"x=-25+%2F+2-5%2Asqrt%2841%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So these expressions approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3.50781059358212 ALIGN=MIDDLE  ALT=\"x=3.50781059358212\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-28.5078105935821 ALIGN=MIDDLE  ALT=\"x=-28.5078105935821\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our possible solutions are:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3.50781059358212 ALIGN=MIDDLE  ALT=\"x=3.50781059358212\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-28.5078105935821 ALIGN=MIDDLE  ALT=\"x=-28.5078105935821\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "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=3.50781059358212 ALIGN=MIDDLE  ALT=\"x=3.50781059358212\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is 3.507 to the nearest thousandth\r<BR>\n" );
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document.write( "-----------------------------\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000=%2820%2B2x%29%2830%2B2x%29 ALIGN=MIDDLE  ALT=\"1000=%2820%2B2x%29%2830%2B2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given area function\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000=%2820%2B2%283.508%29%29%2830%2B2%283.507%29%29 ALIGN=MIDDLE  ALT=\"1000=%2820%2B2%283.508%29%29%2830%2B2%283.507%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > plug in x=3.507\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000=%2820%2B7.016%29%2830%2B7.014%29 ALIGN=MIDDLE  ALT=\"1000=%2820%2B7.016%29%2830%2B7.014%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000=%2827.016%29%2837.014%29 ALIGN=MIDDLE  ALT=\"1000=%2827.016%29%2837.014%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000=999.970224 ALIGN=MIDDLE  ALT=\"1000=999.970224\"   DISABLED_style= \"max-width:90%; height:auto;\" > Since we rounded, this is as close as it gets. So our answer is verified. </SPAN>\n" );
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