document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172937>Question 1172937</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Officer Mark has 300 m of yellow tape to seal off the area of a crime scene. Using the tape, he must divide the area<BR>\n" );
document.write( "into four identical rectangular sections, side by side. What dimensions of the crime scene will maximize the area?<BR>\n" );
document.write( "What is the maximum area that can be enclosed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #798075 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=798075\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Officer Mark has 300 m of yellow tape to seal off the area of a crime scene. Using the tape, he must divide the area into four identical rectangular sections, side by side.<BR>\n" );
document.write( " What dimensions of the crime scene will maximize the area?<BR>\n" );
document.write( "To divide into 4 areas, it requires 5 dividing sides and 2 lengths<BR>\n" );
document.write( "2L + 5w = 300<BR>\n" );
document.write( "simplify, divide by 2<BR>\n" );
document.write( "L + 2.5w = 150<BR>\n" );
document.write( "L = 150 - 2.5w<BR>\n" );
document.write( "Area = L*w<BR>\n" );
document.write( "replace L with (150-2.5w)<BR>\n" );
document.write( "A = w(150-2.5w)<BR>\n" );
document.write( "A = 150w - 2.5w^2<BR>\n" );
document.write( "A quadratic equation where b=150 and a=-2.5<BR>\n" );
document.write( "The max area occurs on the axis of symmetry, find that using x=-b/(2a)<BR>\n" );
document.write( "w = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-150%29%2F%282%2A-2.5%29 ALIGN=MIDDLE  ALT=\"%28-150%29%2F%282%2A-2.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "w = 30 meters is the width<BR>\n" );
document.write( "Find the length<BR>\n" );
document.write( "L = 150 - 2.5(30) <BR>\n" );
document.write( "L = 75 meters is the length<BR>\n" );
document.write( ":<BR>\n" );
document.write( "What is the maximum area that can be enclosed?<BR>\n" );
document.write( " 75 * 30 = 2250 sq meters </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );