document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=357803>Question 357803</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A parking lot is 75 feet wide by 60 feet long. It is being torn up to install a sidewalk of uniform width all the way around. If the area of the new parking lot is 2/3 of the original one, find the width of the sidewalk. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #255572 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=255572\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A parking lot is 75 feet wide by 60 feet long.<BR>\n" );
document.write( " It is being torn up to install a sidewalk of uniform width all the way around.<BR>\n" );
document.write( " If the area of the new parking lot is 2/3 of the original one, find the width of the sidewalk.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the original area; 75 * 60 = 4500 sq/ft<BR>\n" );
document.write( "Find 2/3 of that: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >* 4500 = 3000 sq/ft, is the new parking lot area<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = the width of the sidewalk<BR>\n" );
document.write( "then the dimensions of new parking lot will be: (75-2x) by (60-2x)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "the area equation<BR>\n" );
document.write( "(75-2x)*(60-2x) = 3000 <BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "4500 - 150x - 120x + 4x^2 = 3000<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "4x^2 - 270x + 4500 - 3000 = 0<BR>\n" );
document.write( "4x^2 - 270x + 1500 = 0<BR>\n" );
document.write( "simplify, divide by 2<BR>\n" );
document.write( "2x^2 - 135x + 750 = 0<BR>\n" );
document.write( "Solve for x using the quadratic formula:<BR>\n" );
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;\" > <BR>\n" );
document.write( "In this equation: a=2; b=-135, c=750<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-135%29+%2B-+sqrt%28-135%5E2-4%2A2%2A750+%29%29%2F%282%2A2%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-135%29+%2B-+sqrt%28-135%5E2-4%2A2%2A750+%29%29%2F%282%2A2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28135+%2B-+sqrt%2818225-6000+%29%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%28135+%2B-+sqrt%2818225-6000+%29%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( ":<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28135+%2B-+sqrt%2812225+%29%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%28135+%2B-+sqrt%2812225+%29%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Two solutions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28135+%2B+110.5667%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%28135+%2B+110.5667%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=245.5667%2F4 ALIGN=MIDDLE  ALT=\"245.5667%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 61.4; obviously not a good solution<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28135+-+110.5667%29%2F4+ ALIGN=MIDDLE  ALT=\"x+=+%28135+-+110.5667%29%2F4+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24.43%2F4 ALIGN=MIDDLE  ALT=\"24.43%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 6.1 ft is the width of the side walk<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "We can check this by finding the area with this value<BR>\n" );
document.write( "(75-2(6.1)) * (60-2(6.1)) =<BR>\n" );
document.write( "62.8 * 47.8 = 30001.84 ~ 3000, close enough </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );