document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193348>Question 1193348</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A soccer field has a perimeter of 288 meters and an area of 4,860 square meters. What are the dimensions of the field? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825356 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825356\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A soccer field has a perimeter of 288 meters and an area of 4,860 square meters. <BR>\n" );
document.write( "What are the dimensions of the field?<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "Let x be the length, in meters;  y be the width.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then x + y = 288/2 = 144  (half of the perimeter).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Consider the arithmetic mean of x and y, which is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2By%29%2F2 ALIGN=MIDDLE  ALT=\"%28x%2By%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144%2F2 ALIGN=MIDDLE  ALT=\"144%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 72.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then, obviously,  x = 72+a, y = 72-a  for some value of \"a\"  (x and y are equally remoted from the arithmetic mean).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore, the area of the field is\r\n" );
document.write( "\r\n" );
document.write( "    area = x*y = (72+a)*(72-a) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72%5E2 ALIGN=MIDDLE  ALT=\"72%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5184 - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the area equation is  \r\n" );
document.write( "\r\n" );
document.write( "    5184 - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4860.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From this equation,  find  \"a\"\r\n" );
document.write( "\r\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 5184 - 4860\r\n" );
document.write( "\r\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2 ALIGN=MIDDLE  ALT=\"a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > =     324\r\n" );
document.write( "\r\n" );
document.write( "    a   =  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28324%29 ALIGN=MIDDLE  ALT=\"sqrt%28324%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 18.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus the dimensions of the field are  x = 72+18 = 90 meters  and  y = 72-18 = 54 meters.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "<U>ANSWER</U>.  The dimensions of the field are  90 meters by 54 meters.\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "Solved.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The method showed in my post is non-standard method, &nbsp;which is rarely used in traditional school education.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Its advantage is in that in many cases it allows to get the answer without long calculations - \r<BR>\n" );
document.write( "\n" );
document.write( "practically &nbsp;MENTALLY, &nbsp;as you see in the given case.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "----------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you want to see many other similar solved problems, &nbsp;look into the lessons\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Surface-area/Problems-on-the-area-and-the-perimeter-of-a-rectangle.lesson>Problems on the area and the dimensions of a rectangle</A>\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Surface-area/Three-methods-to-find-the-dimensions-of-a-rectangle-when-the-givens-are-its-perimeter-and-the-area.lesson>Three methods to find the dimensions of a rectangle when its perimeter and the area are given</A>\r<BR>\n" );
document.write( "\n" );
document.write( "in this site.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The first reference is the standard method; &nbsp;the second reference teaches non-standard methods.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site\r<BR>\n" );
document.write( "\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The referred lesson is the part of this online textbook under the topic <BR>\n" );
document.write( "\"<U>Dimensions and the area of rectangles and circles and their elements</U>\".\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Save the link to this online textbook together with its description\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Free of charge online textbook in ALGEBRA-I<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to your archive and use it when it is needed.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );