document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=939075>Question 939075</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A piece of wire 40cm long is to be cut into two pieces. One piece will 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 #572335 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=572335\">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( "We know that the circumference of the circle + the perimeter of the square = 40<BR>\n" );
document.write( "Let x = the circumference of the circle<BR>\n" );
document.write( "Find r in terms of x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2Ar+=+x ALIGN=MIDDLE  ALT=\"2%2Api%2Ar+=+x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%282%2Api%29 ALIGN=MIDDLE  ALT=\"x%2F%282%2Api%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Area+=+pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"Area+=+pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <BR>\n" );
document.write( "therefore<BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A%28x%2F%282%2Api%29%29%5E2 ALIGN=MIDDLE  ALT=\"pi%2A%28x%2F%282%2Api%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A%28x%5E2%2F%284%2Api%5E2%29%29 ALIGN=MIDDLE  ALT=\"pi%2A%28x%5E2%2F%284%2Api%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F%284%2Api%29 ALIGN=MIDDLE  ALT=\"x%5E2%2F%284%2Api%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the area of the circle<BR>\n" );
document.write( ":<BR>\n" );
document.write( "(40-x) = the perimeter of the square<BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2840-x%29%29%2F4 ALIGN=MIDDLE  ALT=\"%28%2840-x%29%29%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >  = one side of the square<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%2840-x%29%29%2F4%29%5E2 ALIGN=MIDDLE  ALT=\"%28%28%2840-x%29%29%2F4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the area of the square<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Total Area<BR>\n" );
document.write( "A(x) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F%284%2Api%29 ALIGN=MIDDLE  ALT=\"x%5E2%2F%284%2Api%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%2840-x%29%29%2F4%29%5E2 ALIGN=MIDDLE  ALT=\"%28%28%2840-x%29%29%2F4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Graph this equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-6%2C+30%2C+-10%2C+100%2C+%28x%5E2%2F%284%2Api%29%29%2B%28%2840-x%29%2F4%29%5E2%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Put this equation into my graphing calc, min occurs when x = 17.6 cm is the piece to make the circle<BR>\n" );
document.write( "therefore the piece of wire to make the square is 40 - 17.6 = 22.4 cm<BR>\n" );
document.write( ";<BR>\n" );
document.write( "Did this make sense to you? let me know; ankor@att.net<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );