document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120090>Question 120090</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi! May I get help with this problem?\r<BR>\n" );
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document.write( "A wire 220 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? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88024 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=88024\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's say the wire is cut into two pieces, one of them is L inches, and the other is 220 - L inches.\r<BR>\n" );
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document.write( "If we take the first piece and form it into a square, each one of the sides of the square will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2F4 ALIGN=MIDDLE  ALT=\"L%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches, so the area of the square will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bs%5D=%28L%2F4%29%5E2 ALIGN=MIDDLE  ALT=\"A%5Bs%5D=%28L%2F4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The area of a circle is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bc%5D=pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A%5Bc%5D=pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but since the circumference of a circle is given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=2%2Api%2Ar ALIGN=MIDDLE  ALT=\"C=2%2Api%2Ar\"   DISABLED_style= \"max-width:90%; height:auto;\" > we can say that the radius of a circle with circumference C is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=C%2F%282%2Api%29 ALIGN=MIDDLE  ALT=\"r=C%2F%282%2Api%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Now we can re-write the circle area formula as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bc%5D=pi%2A%28C%2F%282%2Api%29%29%5E2 ALIGN=MIDDLE  ALT=\"A%5Bc%5D=pi%2A%28C%2F%282%2Api%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then simplify to:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bc%5D=C%5E2%2F%284%2Api%29 ALIGN=MIDDLE  ALT=\"A%5Bc%5D=C%5E2%2F%284%2Api%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bs%5D=A%5Bc%5D ALIGN=MIDDLE  ALT=\"A%5Bs%5D=A%5Bc%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28L%2F4%29%5E2=C%5E2%2F%284%2Api%29 ALIGN=MIDDLE  ALT=\"%28L%2F4%29%5E2=C%5E2%2F%284%2Api%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2%2F16=C%5E2%2F%284%2Api%29 ALIGN=MIDDLE  ALT=\"L%5E2%2F16=C%5E2%2F%284%2Api%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16pi ALIGN=MIDDLE  ALT=\"16pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2AL%5E2=4C%5E2 ALIGN=MIDDLE  ALT=\"pi%2AL%5E2=4C%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take the square root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2Asqrt%28pi%29=2C ALIGN=MIDDLE  ALT=\"L%2Asqrt%28pi%29=2C\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "But we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=220-L ALIGN=MIDDLE  ALT=\"C=220-L\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so substitute:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2Asqrt%28pi%29=2%28220-L%29 ALIGN=MIDDLE  ALT=\"L%2Asqrt%28pi%29=2%28220-L%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Distribute and collect like terms:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%2Asqrt%28pi%29%2B2L=440 ALIGN=MIDDLE  ALT=\"L%2Asqrt%28pi%29%2B2L=440\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Factor out L\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%28sqrt%28pi%29%2B2%29=440 ALIGN=MIDDLE  ALT=\"L%28sqrt%28pi%29%2B2%29=440\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And divide by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28pi%29%2B2 ALIGN=MIDDLE  ALT=\"sqrt%28pi%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28L=440%2F%28sqrt%28pi%29%2B2%29%29 ALIGN=MIDDLE  ALT=\"green%28L=440%2F%28sqrt%28pi%29%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  inches\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=220-L ALIGN=MIDDLE  ALT=\"C=220-L\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=220-%28440%2F%28sqrt%28pi%29%2B2%29%29 ALIGN=MIDDLE  ALT=\"C=220-%28440%2F%28sqrt%28pi%29%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify with LCD of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28pi%29%2B2 ALIGN=MIDDLE  ALT=\"sqrt%28pi%29%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=%28220%28sqrt%28pi%29%2B2%29-440%29%2F%28sqrt%28pi%29%2B2%29 ALIGN=MIDDLE  ALT=\"C=%28220%28sqrt%28pi%29%2B2%29-440%29%2F%28sqrt%28pi%29%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28C=220%2Asqrt%28pi%29%2F%28sqrt%28pi%29%2B2%29%29 ALIGN=MIDDLE  ALT=\"green%28C=220%2Asqrt%28pi%29%2F%28sqrt%28pi%29%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches\r<BR>\n" );
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document.write( "Check your answer:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bs%5D=%28%28440%2F%28sqrt%28pi%29%2B2%29%29%2F4%29%5E2=110%5E2%2F%28sqrt%28pi%29%2B2%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bc%5D=pi%2A%28%28220%2Asqrt%28pi%29%2F%28sqrt%28pi%29%2B2%29%29%2F%282%2Api%29%29%5E2=pi%2A%28110%2F%28%28sqrt%28pi%29%2B2%29%2Asqrt%28pi%29%29%29%5E2=%28110%5E2%29%2F%28sqrt%28pi%29%2B2%29%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.  So the areas are equal\r<BR>\n" );
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document.write( "Now add the two lengths:  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28220%2Asqrt%28pi%29%2F%28sqrt%28pi%29%2B2%29%29%2B%28440%2F%28sqrt%28pi%29%2B2%29%29 ALIGN=MIDDLE  ALT=\"%28220%2Asqrt%28pi%29%2F%28sqrt%28pi%29%2B2%29%29%2B%28440%2F%28sqrt%28pi%29%2B2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28220%2Asqrt%28pi%29%2B440%29%2F%28sqrt%28pi%29%2B2%29 ALIGN=MIDDLE  ALT=\"%28220%2Asqrt%28pi%29%2B440%29%2F%28sqrt%28pi%29%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28220%28sqrt%28pi%29%2B2%29%29%2F%28sqrt%28pi%29%2B2%29=220 ALIGN=MIDDLE  ALT=\"%28220%28sqrt%28pi%29%2B2%29%29%2F%28sqrt%28pi%29%2B2%29=220\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so the two lengths add to 220. \r<BR>\n" );
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document.write( "Answer checks.\r<BR>\n" );
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document.write( "Final note:  the expressions for L and C developed above are the exact answers.  If you want to use a calculator to develop a decimal approximation of the answer, remember that you should never express an answer based on calculations involving measurements to greater precision than the least precise measurement given.  Since the length of the wire was expressed to the nearest inch, you should express your answer to the nearest inch as well. </SPAN>\n" );
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