document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=237229>Question 237229</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the ratio of the square's area to the circle's area if the square and circle have equal perimeter? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #174455 by </B><A HREF=/tutors/aboutme.mpl?userid=rapaljer><B>rapaljer(4671)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rapaljer><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=rapaljer><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=174455\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let r= radius of the circle, and let x = side of the square.\r<BR>\n" );
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document.write( "Perimeter of circle = <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;\" >.\r<BR>\n" );
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document.write( "Perimeter of rectangle = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x ALIGN=MIDDLE  ALT=\"4x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If the perimeters are equal, then \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2Ar=4x ALIGN=MIDDLE  ALT=\"2%2Api%2Ar=4x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "You need to find the ratio of the area of the square to the area of the circle.\r<BR>\n" );
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document.write( "Area of circle = <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( "Area of square =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Ratio of area of square to area of circle = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%2F%28pi%2Ar%5E2%29 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%2F%28pi%2Ar%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Before proceeding, just for fun (and it will be helpful later!!), find the ratio of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2Fr ALIGN=MIDDLE  ALT=\"x%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" > using the equation above <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x=2%2Api%2Ar ALIGN=MIDDLE  ALT=\"4x=2%2Api%2Ar\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Divide both sides by <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;\" >:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%284x%29%2F%282%2Api%2Ar%29=1 ALIGN=MIDDLE  ALT=\"+%284x%29%2F%282%2Api%2Ar%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide out the 2 factor:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x%29%2F%28pi%2Ar%29=+1 ALIGN=MIDDLE  ALT=\"%282x%29%2F%28pi%2Ar%29=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Divide both sides by 2, and  multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   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=x%2Fr=+pi%2F2 ALIGN=MIDDLE  ALT=\"x%2Fr=+pi%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "NOW:\r<BR>\n" );
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document.write( "RATIO of AREAS= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28Area+of+Square%29%2F%28Area+of+Circle%29 ALIGN=MIDDLE  ALT=\"%28Area+of+Square%29%2F%28Area+of+Circle%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2%29%2F%28pi%2Ar%5E2%29=%281%2Fpi%29%2A%28x%2Fr%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E2%29%2F%28pi%2Ar%5E2%29=%281%2Fpi%29%2A%28x%2Fr%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fpi%29%2A%28pi%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"%281%2Fpi%29%2A%28pi%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fpi%29%2A%28pi%5E2%2F2%5E2%29 ALIGN=MIDDLE  ALT=\"%281%2Fpi%29%2A%28pi%5E2%2F2%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=pi%2F4 ALIGN=MIDDLE  ALT=\"pi%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This is quite an interesting problem!  You may want to get a second opinion on it!!  \r<BR>\n" );
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document.write( "Dr. Robert J. Rapalje\r<BR>\n" );
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