document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=263596>Question 263596</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A piece of wire 40cm long is to be cut into two pieces. One piece wil be bent to form a circle; the other will be bent to form a square.  Find the lengths of the two pieces that cause the sum of the area of the circle and square to be a minimum. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #194300 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=194300\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A piece of wire 40cm long is to be cut into two pieces.<BR>\n" );
document.write( " One piece will be bent to form a circle; the other will be bent to form a square.<BR>\n" );
document.write( " Find the lengths of the two pieces that cause the sum of the area of the circle and square to be a minimum.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = circumference of the circle<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(40-x) = perimeter of the square<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the radius of the circle<BR>\n" );
document.write( "r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%282pi%29 ALIGN=MIDDLE  ALT=\"x%2F%282pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the area of the circle<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%28x%2F%282pi%29%29%5E2+ ALIGN=MIDDLE  ALT=\"pi%28x%2F%282pi%29%29%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%28x%5E2%2F%284pi%5E2%29%29 ALIGN=MIDDLE  ALT=\"pi%28x%5E2%2F%284pi%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cancel pi<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F%284pi%29 ALIGN=MIDDLE  ALT=\"x%5E2%2F%284pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the area of the square:<BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2840-x%29%2F4%29%5E2 ALIGN=MIDDLE  ALT=\"%28%2840-x%29%2F4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "a = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+80x+%2B+1600%29%2F16 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+80x+%2B+1600%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Total area<BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F%284pi%29 ALIGN=MIDDLE  ALT=\"x%5E2%2F%284pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2+-+80x+%2B+1600%29%2F16 ALIGN=MIDDLE  ALT=\"%28x%5E2+-+80x+%2B+1600%29%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Change to decimals, easier to combine like terms<BR>\n" );
document.write( "A = .07958x^2 + .0625x^2 - 5x + 100<BR>\n" );
document.write( "A = .14208x^2 - 5x + 100<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the axis of symmetry [x = -b/(2a)]<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-%28-5%29%29%2F%282%2A.14208%29 ALIGN=MIDDLE  ALT=\"%28-%28-5%29%29%2F%282%2A.14208%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F.28416 ALIGN=MIDDLE  ALT=\"5%2F.28416\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x ~ 17.6 inches, the piece of wire creating a circle<BR>\n" );
document.write( "and<BR>\n" );
document.write( "40 - 17.6 = 22.4 inches, the piece of wire creating the square<BR>\n" );
document.write( ":<BR>\n" );
document.write( "These lengths should give minimum area of the circle and square together </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );