document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=237228>Question 237228</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the perimeter of a circle is equal to that of a square, then the ratio of their<BR>\n" );
document.write( "areas is<BR>\n" );
document.write( "(A) 22 : 7 (B) 14 : 11 (C) 7 : 22 (D) 11: 14<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #174465 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=174465\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the ratio appears to be 11/14 or 14/11 depending on who's on top.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if it's the ratio of the area of the circle to the area of the square, then the ratio is 14 to 11 = 14/11\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since they mentioned the circle first, i would assume they want the ratio of the area of the circle to the area of the square.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that would be 14 : 11 which is equivalent to 1.2727272727.....\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here's how.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "statement is that the perimeter of the circle equals the perimeter of the square.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that means that:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4*s = 2*pi*r\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides by 2*pi to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "r = 4*s/2*pi = 2*s/pi\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "area of a circle is equal to pi*r^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "area of a square is equal to s^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ratio of the area of a circle to a square is pi*r^2/s^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since r = 2*s/pi that becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "ratio of the area of a circle to a square is pi*(2*s/pi)^2 / s^2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(pi*(2*s)^2)/(pi)^2 / s^2 which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(4*s^2/pi) / s^2 which becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4/pi\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the ratio of the area of the circle to the area of the square is 4/pi which is equivalent to 1.273239545\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1.273239545 is very close to 1.2727272727....\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the differnce is in the rounding.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you take 4/pi * 11 you will get 14.00563499\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "14/11 was really 14.00563499 but was truncated to the nearest digit.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "none of the other answers even came close.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i would go with 14 / 11 as the correct ratio.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that would be answer (B)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "11 / 14 could be an answer if the ratio was the area of the square to the area of the circle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "they did not specify directly.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "they only implied, by mentioning the circle first.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the question should have read:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If the perimeter of a circle is equal to that of a square, then the ratio of the area of the circle to the square is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "(A) 22 : 7 (B) 14 : 11 (C) 7 : 22 (D) 11: 14\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );