document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=818741>Question 818741</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A high school is planining to build a new playing field surrounded by a running track. The track coach wants 2 laps around the track to be 1000m. The football coach wants the rectangular infield to be as large as possible. Can both coaches be satisfied? State the dimensions.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #492759 by </B><A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><B>TimothyLamb(4379)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TimothyLamb><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=TimothyLamb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=492759\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 2(2L + 2w) = 1000<BR>\n" );
document.write( "4L + 4w = 1000<BR>\n" );
document.write( "4w = 1000 - 4L<BR>\n" );
document.write( "w = 250 - L<BR>\n" );
document.write( "a = Lw<BR>\n" );
document.write( "---<BR>\n" );
document.write( "a = Lw<BR>\n" );
document.write( "a = L(250 - L)<BR>\n" );
document.write( "a = 250L - LL<BR>\n" );
document.write( "a(L) = -L^2 + 250L<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the above quadratic equation is in standard form, with a=-1, b=250, and c=0<BR>\n" );
document.write( "---<BR>\n" );
document.write( "to solve the quadratic equation, by using the quadratic formula, plug this:<BR>\n" );
document.write( "-1 250 0<BR>\n" );
document.write( "into this: https://sooeet.com/math/quadratic-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the quadratic vertex is a maximum at: ( L= 125, a(L)= 15625 )<BR>\n" );
document.write( "---<BR>\n" );
document.write( "the maximum area of the infield is: a(L) = a(125) = 15625 sq.m (that's what football coach wants)<BR>\n" );
document.write( "L = 125 m<BR>\n" );
document.write( "w = a(125)/125= 15625 /125 = 125 m<BR>\n" );
document.write( "---<BR>\n" );
document.write( "check track perimeter:<BR>\n" );
document.write( "p = 2L + 2w<BR>\n" );
document.write( "p = 2(125) + 2(125)<BR>\n" );
document.write( "p = 500<BR>\n" );
document.write( "two laps around track = 2p = 1000 m (correct, that's what track coach wants)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve and graph linear equations:<BR>\n" );
document.write( "https://sooeet.com/math/linear-equation-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Solve quadratic equations, quadratic formula:<BR>\n" );
document.write( "https://sooeet.com/math/quadratic-formula-solver.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Convert fractions, decimals, and percents:<BR>\n" );
document.write( "https://sooeet.com/math/fraction-decimal-percent.php<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Calculate and graph the linear regression of any data set:<BR>\n" );
document.write( "https://sooeet.com/math/linear-regression.php </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );