document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=504167>Question 504167</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tarry is a farmer. She decides to make a circular pen for her sheep. She uses all of the fencing she has to make the fence (i.e. circumference =100) She then decides to make a square enclosure inside the circle, so that the corners of the square just touch the circle. What would be the squares perimeter?  <BR>\n" );
document.write( "She then decides to make a square enclosure around the outside of the circle. What would the outside squares perimeter be?\r<BR>\n" );
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document.write( "I found the radius of the circle=15.92.<BR>\n" );
document.write( "I found the diameter of the circle=31.8.<BR>\n" );
document.write( "The area of the circle 795.\r<BR>\n" );
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document.write( "But im lost on getting any information of the square inside the circles.<BR>\n" );
document.write( "My thoughts on a diameter is diagnol line inside the circle where it can also go straight across and i think that is whats throwing me off. <BR>\n" );
document.write( "My guess id the perimeter of the inner square is 10.<BR>\n" );
document.write( "Please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #339540 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=339540\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you're on the right track.<BR>\n" );
document.write( "here's a picture of what you're trying to do.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2011/sep253.jpg\" alt = \"$$$$$\" /><BR>\n" );
document.write( "the inscribed square will have a diagonal that is a diameter of the circle.<BR>\n" );
document.write( "the circumscribed square will have an apothem that is a radius of the circle.<BR>\n" );
document.write( "the circumference of your circle is 100<BR>\n" );
document.write( "the formula for the circumference is 2*pi*r<BR>\n" );
document.write( "you get:<BR>\n" );
document.write( "2*pi*r = 100<BR>\n" );
document.write( "solve for r to get:<BR>\n" );
document.write( "r = 100/(2*pi) = 15.91549431<BR>\n" );
document.write( "the questions you are being asked are:\r<BR>\n" );
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document.write( "Tarry is a farmer. She decides to make a circular pen for her sheep. She uses all of the fencing she has to make the fence (i.e. circumference =100) She then decides to make a square enclosure inside the circle, so that the corners of the square just touch the circle. What would be the squares perimeter?<BR>\n" );
document.write( "She then decides to make a square enclosure around the outside of the circle. What would the outside squares perimeter be? \r<BR>\n" );
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document.write( "without getting into the details, the perimeter of the inscribed square will be equal to 4 * 22.5079079 = 90.03163162\r<BR>\n" );
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document.write( "without getting into details again, the perimeter of the circumscribed square will be equal to 4 * 31.83098862 = 127.3239545\r<BR>\n" );
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document.write( "now the details.....\r<BR>\n" );
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document.write( "the diagonal of the inscribed square is the diameter of the circle.<BR>\n" );
document.write( "this makes the diagonal equal to 2 times the radius you found earlier which makes it equal to 15.92 * 2 = 31.83.<BR>\n" );
document.write( "it's not 31.84 because i used number from the calculator that haven't been rounded yet.\r<BR>\n" );
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document.write( "this diagonal is the hypotenuse of a right triangle whose legs are the sides of the square.<BR>\n" );
document.write( "we use the pythagorean formula to find the length of the legs.<BR>\n" );
document.write( "the formula becomes:<BR>\n" );
document.write( "2*L^2 = 31.83^2.<BR>\n" );
document.write( "we divide this formula by 2 to get:<BR>\n" );
document.write( "L^2 = 15.92^2 / 2<BR>\n" );
document.write( "that gets us:<BR>\n" );
document.write( "L = 22.5079079<BR>\n" );
document.write( "4 times that is the perimeter of the square which equals 90.03163162.<BR>\n" );
document.write( "L stands for Leg of the right triangle.<BR>\n" );
document.write( "L is also the side of the square.<BR>\n" );
document.write( "i will follow up with another picture to show you.\r<BR>\n" );
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document.write( "the circumscribed square is tangent to the circle at it's apothem.<BR>\n" );
document.write( "the apothem turns out to be the length of the radius of the circle.<BR>\n" );
document.write( "extend that across and you have the length of a side of the circumscribed square.<BR>\n" );
document.write( "times that by 4 and you get the perimeter of the circumscribed square.<BR>\n" );
document.write( "it turns out to be 4 * 31.83 = 127.3239545<BR>\n" );
document.write( "the picture below shows you the inscribed square measurements and the circumscribed square measurements.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2011/sep254.jpg\" alt = \"$$$$$\" />\r<BR>\n" );
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document.write( "here's a reference on the apothem of a polygon in case you're not familiar with the term.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"http://www.mathopenref.com/apothem.html\" target = \"_blank\">http://www.mathopenref.com/apothem.html</a> </SPAN>\n" );
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