document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149136>Question 149136</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Alex's dog, Fluffy, is tied witha 20 foot rope to the center of the back wall of the shed, which has dimensions of 14 ft by 18 ft. If trhe back wall is the longer wall, over what area can Fluffy play, to the nearest square foot? Would your answer change if the back wall was 14 ft instead?  \r<BR>\n" );
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document.write( "Thank you so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109404 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=109404\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the rope is stretched tight, Fluffy can reach everything at<BR>\n" );
document.write( "a distance of 20' from the center of the 18' wall to the left and right<BR>\n" );
document.write( "as long as Fluffy doesn't start to bend the rope around the corners<BR>\n" );
document.write( "So far that is a semicircle with area of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2+%2F+2 ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+20 ALIGN=MIDDLE  ALT=\"r+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.1416%2A400+%2F+2+=+628.32 ALIGN=MIDDLE  ALT=\"3.1416%2A400+%2F+2+=+628.32\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft2<BR>\n" );
document.write( "When the rope bends around the corner, it's radius becomes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+-+%2818%2F2%29 ALIGN=MIDDLE  ALT=\"20+-+%2818%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+-+9+=+11 ALIGN=MIDDLE  ALT=\"20+-+9+=+11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and Fluffy has to stop when he gets to the side<BR>\n" );
document.write( "wall. That is a quadrant (1/4th) of a circle on each side with total<BR>\n" );
document.write( "area of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A11%5E2+%2F+4+%2B+pi%2A11%5E2+%2F+4 ALIGN=MIDDLE  ALT=\"pi%2A11%5E2+%2F+4+%2B+pi%2A11%5E2+%2F+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A11%5E2+%2F+2+ ALIGN=MIDDLE  ALT=\"pi%2A11%5E2+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.1416%2A121+%2F+2 ALIGN=MIDDLE  ALT=\"3.1416%2A121+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=190.067 ALIGN=MIDDLE  ALT=\"190.067\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft2<BR>\n" );
document.write( "The sum of these areas is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=628.32+%2B+190.067+=+818.39 ALIGN=MIDDLE  ALT=\"628.32+%2B+190.067+=+818.39\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft2<BR>\n" );
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document.write( "If the back wall is 14', the answer does change.<BR>\n" );
document.write( "The big semicircle is still <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=628.32 ALIGN=MIDDLE  ALT=\"628.32\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft2,<BR>\n" );
document.write( "but the area of the side quadrants is bigger<BR>\n" );
document.write( "the radius is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20+-+%2814%2F2%29 ALIGN=MIDDLE  ALT=\"20+-+%2814%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+20+-+7+=+13 ALIGN=MIDDLE  ALT=\"+20+-+7+=+13\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The area is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A13%5E2+%2F+4+%2B+pi%2A13%5E2+%2F+4 ALIGN=MIDDLE  ALT=\"pi%2A13%5E2+%2F+4+%2B+pi%2A13%5E2+%2F+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A13%5E2+%2F+2 ALIGN=MIDDLE  ALT=\"pi%2A13%5E2+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3.1416+%2A+169+%2F+2+=+265.46 ALIGN=MIDDLE  ALT=\"3.1416+%2A+169+%2F+2+=+265.46\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, the total area is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=628.32+%2B+265.46+=+893.78 ALIGN=MIDDLE  ALT=\"628.32+%2B+265.46+=+893.78\"   DISABLED_style= \"max-width:90%; height:auto;\" > ft2 </SPAN>\n" );
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