document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=99587>Question 99587</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Construction. A garden area is 30ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400ft^2, what is teh 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 #72452 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=72452\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A  garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400 ft^2, what is the width of the path? <BR>\n" );
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document.write( "Draw diagram of this; label the outside dimensions of the rectangle 30 by 20.<BR>\n" );
document.write( "Label the width of the path as x, it will be apparent that the dimensions of<BR>\n" );
document.write( "the garden (inside the path), will be (30-2x) by (20-2x)<BR>\n" );
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document.write( "The area of the garden is given as 400 sq/ft<BR>\n" );
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document.write( "A simple area equation:<BR>\n" );
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document.write( "length times width = 400 sq/ft<BR>\n" );
document.write( "(30-2x) * (20-2x)  = 400<BR>\n" );
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document.write( "FOIL:<BR>\n" );
document.write( "600 - 60x - 40x + 4x^2 = 400<BR>\n" );
document.write( "4x^2 - 100x + 600 = 400<BR>\n" );
document.write( "4x^2 - 100x + 600 - 400 = 0<BR>\n" );
document.write( "4x^2 - 100x + 200 = 0; a quadratic equation<BR>\n" );
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document.write( "Simplify, divide by 4 and you have:<BR>\n" );
document.write( "x^2 - 25x + 50 = 0<BR>\n" );
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document.write( "We need to use the quadratic formula to solve this: a=1; b=-25;; c=50<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-25%29+%2B-+sqrt%28+-25%5E2-4%2A1%2A50+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-25%29+%2B-+sqrt%28+-25%5E2-4%2A1%2A50+%29%29%2F%282%2A1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28%2B25+%2B-+sqrt%28625+-+200+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28%2B25+%2B-+sqrt%28625+-+200+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2825+%2B-+sqrt%28425+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%2825+%2B-+sqrt%28425+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Two solutions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2825+%2B+20.62%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%2825+%2B+20.62%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+45.62%2F2 ALIGN=MIDDLE  ALT=\"x+=+45.62%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 22.8, not a possible solution, obviously<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2825+-+20.62%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%2825+-+20.62%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+4.38%2F2 ALIGN=MIDDLE  ALT=\"x+=+4.38%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 2.19 ft is the width of the path<BR>\n" );
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document.write( "Check our solution by finding the area of the garden<BR>\n" );
document.write( "We have to subtract 2x from the outside dimensions: 2*2.19 = 4.38<BR>\n" );
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document.write( "(30-4.38) * (20-4.38) =<BR>\n" );
document.write( "  25.62  * 15.62 = 400.2 ~ 400 sq/ft<BR>\n" );
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