document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=964092>Question 964092</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular park measuring 31 yards by 27yards is surrounded by a trial of uniform width. If the area of the park and the trial combined is 2205 square yards, 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 #588987 by </B><A HREF=/tutors/aboutme.mpl?userid=addingup><B>addingup(3677)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=addingup><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=addingup><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=588987\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) The trail around the park is all the same width, like the frame on a picture.<BR>\n" );
document.write( "2) The area of a rectangle = l x w<BR>\n" );
document.write( "3) A rectangle has 2 lengths and 2 widths. Let's call the width of the trail x:<BR>\n" );
document.write( "(31+2x)(27+2x)= 2205 Multiply (FOIL)<BR>\n" );
document.write( "31*27+31*2x+2x*27+4x^2 = 2205<BR>\n" );
document.write( "= 837+62x+54x+4x^2 = 2205<BR>\n" );
document.write( "=837+116x+4x^2 = 2205 Let's rewrite as a quadratic polynomial:<BR>\n" );
document.write( "4x^2+116x+837= 2205 Divide both sides by 4:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B29x%2B837%2F4=+%282205%2F4%29 ALIGN=MIDDLE  ALT=\"x%5E2%2B29x%2B837%2F4=+%282205%2F4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now solve by completing the square. Subtract 837/4 from both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B29x=+%282205-837%29%2F4 ALIGN=MIDDLE  ALT=\"x%5E2%2B29x=+%282205-837%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B29x=+1368%2F4 ALIGN=MIDDLE  ALT=\"x%5E2%2B29x=+1368%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now divide on right:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B29x=+342 ALIGN=MIDDLE  ALT=\"x%5E2%2B29x=+342\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 342 from both sides:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B29x-342=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B29x-342=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor the equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-9%29%28x%2B38%29=+0 ALIGN=MIDDLE  ALT=\"%28x-9%29%28x%2B38%29=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now we have two possible answers<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-9=+0 ALIGN=MIDDLE  ALT=\"x-9=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B38=+0 ALIGN=MIDDLE  ALT=\"x%2B38=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+9 ALIGN=MIDDLE  ALT=\"x=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=+-38 ALIGN=MIDDLE  ALT=\"x=+-38\"   DISABLED_style= \"max-width:90%; height:auto;\" > We know our answer cannot be negative, so we have that the trail is 9 wide. Let's prove it<BR>\n" );
document.write( "Length: 31+ 2(9)= 49<BR>\n" );
document.write( "Width: 27+2(9)= 45<BR>\n" );
document.write( "Area of the park with the trail: <BR>\n" );
document.write( "49*45= 2205 We've got the correct answer. See the sketch I made you:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=addingup&illustration_name=A_park.JPG\"><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );