document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=940576>Question 940576</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A field contains 48 acres. If it were 12 rods wider and 32 rods shorter, it would still contain 48 acres. Find the number of fencing needed to enclose 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 #573515 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=573515\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A field contains 48 acres.<BR>\n" );
document.write( " If it were 12 rods wider and 32 rods shorter, it would still contain 48 acres.<BR>\n" );
document.write( " Find the number of fencing needed to enclose the field?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "let L = the length of the field in rods<BR>\n" );
document.write( "let w = the width of the field in rods<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the number of sq/ft in 48 acres<BR>\n" );
document.write( "43560 * 48 = 2090880 sq/ft<BR>\n" );
document.write( ":<BR>\n" );
document.write( "1 rod = 16.5 ft, one sq/rod = 16.5^2 = 272.25 sq/ft<BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2090880%2F272.25 ALIGN=MIDDLE  ALT=\"2090880%2F272.25\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 7680 sq/rds in 48 acres<BR>\n" );
document.write( ":<BR>\n" );
document.write( "two equations<BR>\n" );
document.write( " L * W = 7680<BR>\n" );
document.write( " L = 7680/W<BR>\n" );
document.write( " and<BR>\n" );
document.write( "(L-32)*(W+12) = 7680<BR>\n" );
document.write( "FOIL<BR>\n" );
document.write( "LW + 12L - 32W - 384 = 7680<BR>\n" );
document.write( "We know LW = 7680<BR>\n" );
document.write( "7680 + 12L - 32W - 384 = 7680<BR>\n" );
document.write( "subtract 7680 from both sides<BR>\n" );
document.write( "12L - 32W - 384= 0<BR>\n" );
document.write( "simplify, divide by 4<BR>\n" );
document.write( "3L - 8W - 96<BR>\n" );
document.write( "Replace L with 7680/W<BR>\n" );
document.write( "3<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7680%2Fw ALIGN=MIDDLE  ALT=\"7680%2Fw\"   DISABLED_style= \"max-width:90%; height:auto;\" > - 8W - 96 = 0<BR>\n" );
document.write( "multiply both sides by w<BR>\n" );
document.write( "23040 - 8w^2 - 96w = 0<BR>\n" );
document.write( "A quadratic equation<BR>\n" );
document.write( "-8w^2 - 96w + 23040 = 0<BR>\n" );
document.write( "Using the quadratic formula, I got a positive solution of<BR>\n" );
document.write( "w = 48 rods is the width<BR>\n" );
document.write( "and<BR>\n" );
document.write( "7680/48 = 160 rods is the length<BR>\n" );
document.write( ":<BR>\n" );
document.write( "See if that checks out: (48+12)*(160-32) = 7680 also<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"Find the number of fencing needed to enclose the field?\"<BR>\n" );
document.write( "2(160) + 2(48) = 416 rods of fencing required. That's 16.5*416 = 6864 ft<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );