document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=403986>Question 403986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A wire 310 in. long is cut into two pieces. One piece is formed into a square and the other into a circle. If the two figures have the same area, what are the lengths of the two pieces of wire (to the nearest tenth of an inch)?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #285638 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=285638\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A wire 310 in. long is cut into two pieces. One piece is formed into a square and the other into a circle.<BR>\n" );
document.write( "If the two figures have the same area, what are the lengths of the two pieces of wire (to the nearest tenth of an inch)?<BR>\n" );
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document.write( "Let s = the side of the square<BR>\n" );
document.write( "then<BR>\n" );
document.write( "4s = the perimeter of the square<BR>\n" );
document.write( "s^2 = the area of the square<BR>\n" );
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document.write( "Let r = the radius of the circle<BR>\n" );
document.write( "then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2Ar ALIGN=MIDDLE  ALT=\"2%2Api%2Ar\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the circumference of the circle<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = area of the circle<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"the two figures have the same area,<BR>\n" );
document.write( "s^2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28pi%2Ar%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28pi%2Ar%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( ":<BR>\n" );
document.write( "\"A wire 310 in. long is cut into two pieces.\"<BR>\n" );
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document.write( "Perimeter + Circumference = 310 inches<BR>\n" );
document.write( "4s + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2Ar ALIGN=MIDDLE  ALT=\"2%2Api%2Ar\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 310<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Replace s with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28pi%2Ar%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28pi%2Ar%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28sqrt%28pi%2Ar%5E2%29%29+%2B+%282%2Api%2Ar%29 ALIGN=MIDDLE  ALT=\"4%28sqrt%28pi%2Ar%5E2%29%29+%2B+%282%2Api%2Ar%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 310<BR>\n" );
document.write( ":<BR>\n" );
document.write( "simplify, divide by 2, Extract r<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2r%28sqrt%28pi%29%29+%2B+%28pi%2Ar%29 ALIGN=MIDDLE  ALT=\"2r%28sqrt%28pi%29%29+%2B+%28pi%2Ar%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 155<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Change pi to decimal values<BR>\n" );
document.write( "2r(1.772) + r(3.1416) = 155<BR>\n" );
document.write( "3.545r + 3.1416r = 155<BR>\n" );
document.write( "6.6865r = 155<BR>\n" );
document.write( "r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=155%2F6.6865 ALIGN=MIDDLE  ALT=\"155%2F6.6865\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "r = 23.18<BR>\n" );
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document.write( "Find the circumference<BR>\n" );
document.write( "C = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2A23.18 ALIGN=MIDDLE  ALT=\"2%2Api%2A23.18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "C = 145.7 inches the length of the wire to make the circle<BR>\n" );
document.write( "then<BR>\n" );
document.write( "310 - 145.7 = 164.3 inches is the length to make the square<BR>\n" );
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document.write( "Check this by finding the area of circle and the square<BR>\n" );
document.write( "Square: (164.3/4)^2 = 1687.155 sq/inches<BR>\n" );
document.write( "Circle: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A23.18%5E2 ALIGN=MIDDLE  ALT=\"pi%2A23.18%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1688.0 sq/inches, discrepancy is from rounding off\r<BR>\n" );
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document.write( " </SPAN>\n" );
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