document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202100>Question 1202100</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A dog trainer has 100 ft of fencing that will be used to create a rectangular work area for dogs. If the trainer wants to enclose an area of 504 ft2, what will be the dimensions of the work area? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836738 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=836738\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <font color=red>14 ft by 36 ft</font>\r<BR>\n" );
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document.write( "Work Shown:\r<BR>\n" );
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document.write( "x = width<BR>\n" );
document.write( "y = height\r<BR>\n" );
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document.write( "P = perimeter of the rectangle<BR>\n" );
document.write( "P = 2*(width + height)<BR>\n" );
document.write( "P = 2*(x + y)<BR>\n" );
document.write( "Replace P with 100 as this is the perimeter, aka amount of fencing<BR>\n" );
document.write( "100 = 2(x + y)<BR>\n" );
document.write( "100/2 = x + y<BR>\n" );
document.write( "50 = x + y<BR>\n" );
document.write( "y = 50-x\r<BR>\n" );
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document.write( "A = area of the rectangle<BR>\n" );
document.write( "A = width*height<BR>\n" );
document.write( "A = x*y<BR>\n" );
document.write( "A = x*(50-x)<BR>\n" );
document.write( "A = 50x-x^2<BR>\n" );
document.write( "A = -x^2+50x<BR>\n" );
document.write( "Plug in A = 504 which is the desired area.<BR>\n" );
document.write( "504 = -x^2+50x<BR>\n" );
document.write( "0 = -x^2+50x-504<BR>\n" );
document.write( "-x^2+50x-504 = 0<BR>\n" );
document.write( "-(x^2-50x+504) = 0<BR>\n" );
document.write( "x^2-50x+504 = 0\r<BR>\n" );
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document.write( "You could take a trial-and-error approach to factoring, but I think the quadratic formula is more efficient.<BR>\n" );
document.write( "Plug in a = 1, b = -50, c = 504<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-50%29+%2B-+sqrt%28%28-50%29%5E2+-+4%281%29%28504%29%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-50%29+%2B-+sqrt%28%28-50%29%5E2+-+4%281%29%28504%29%29%29%2F%282%281%29%29\"   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+=+%2850+%2B-+sqrt%282500-2016%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2850+%2B-+sqrt%282500-2016%29%29%2F%282%281%29%29\"   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+=+%2850+%2B-+22%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2850+%2B-+22%29%2F%282%29\"   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+=+%2850+%2B+22%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%2850+%2B+22%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+=+%2850+-+22%29%2F%282%29 ALIGN=MIDDLE  ALT=\"+x+=+%2850+-+22%29%2F%282%29\"   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+=+%2872%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%2872%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+=+%2828%29%2F%282%29 ALIGN=MIDDLE  ALT=\"+x+=+%2828%29%2F%282%29\"   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+=+36+ ALIGN=MIDDLE  ALT=\"x+=+36+\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+14 ALIGN=MIDDLE  ALT=\"+x+=+14\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If x = 36, then y = 50-x = 50-36 = 14<BR>\n" );
document.write( "If x = 14, then y = 50-x = 50-14 = 36\r<BR>\n" );
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document.write( "The rectangle is <font color=red>14 ft by 36 ft</font>\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "Perimeter = 2*(14+36) = 2*50 = 100<BR>\n" );
document.write( "Area = 14*36 = 504<BR>\n" );
document.write( "The answers are confirmed.<BR>\n" );
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