document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=881310>Question 881310</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cow is tied to a corner of a fenced rectangular plot of length 40m and breadth 14m.The length of the rope is 21m.Find the total area that it can graze?\r<BR>\n" );
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document.write( "I want proper solution with figure. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #532128 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=532128\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In the popular problem where the cow is tied to the corner of a rectangular restricted area, the cow is on the outside and is tied to the corner of a barn.<BR>\n" );
document.write( "Your cow may be tied inside a fenced rectangular plot, and that would be a different problem.<BR>\n" );
document.write( "I'll discuss both, but see if I make sense, and see if I calculated right, because I am prone to making mistakes.<BR>\n" );
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document.write( "If the cow is inside that rectangular plot:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C200%2C-45%2C27%2C-26%2C22%2C%0D%0Arectangle%280%2C0%2C-40%2C-14%29%2Cgreen%28line%28-15%2C-13.3%2C-0.7%2C-0.7%29%29%2C%0D%0Aarc%280%2C0%2C42%2C42%2C138.2%2C180%29%2C%0D%0Alocate%280%2C-6%2C14%29%2Clocate%28-11%2C4%2C21%29%2C%0D%0Ared%28circle%280%2C0%2C1%29%29%2Cred%28circle%28-21%2C0%2C1%29%29%2C%0D%0Ared%28circle%28-15.65%2C-14%2C1%29%29%2C%0D%0Alocate%281%2C2%2Cred%28X%29%29%2Clocate%28-23%2C-1%2Cred%28A%29%29%2C%0D%0Alocate%28-16.5%2C-14.5%2Cred%28B%29%29%2Clocate%28-7.8%2C-7%2Cgreen%2821%29%29%2C%0D%0Alocate%281.5%2C-12%2Cred%28Y%29%29%2Cred%28circle%280%2C-14%2C1%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > With the rope tight, a cow, tied at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28X%29 ALIGN=MIDDLE  ALT=\"red%28X%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , can circle from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28A%29 ALIGN=MIDDLE  ALT=\"red%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28B%29 ALIGN=MIDDLE  ALT=\"red%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So the cow can graze the X-centered wedge from A to B. and the right triangle XYB.<BR>\n" );
document.write( "We can find the angle YXB from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28YXB%29=14%2F21=2%2F3 ALIGN=MIDDLE  ALT=\"cos%28YXB%29=14%2F21=2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That angle measures about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48.19%5Eo ALIGN=MIDDLE  ALT=\"48.19%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The sine of that angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%281-%282%2F3%29%5E2%29=sqrt%281-4%2F9%29=sqrt%285%2F9%29=sqrt%285%2F9%29 ALIGN=MIDDLE  ALT=\"sqrt%281-%282%2F3%29%5E2%29=sqrt%281-4%2F9%29=sqrt%285%2F9%29=sqrt%285%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the area of triangle XYB (in square meters) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%2914%2A21%28sqrt%285%29%2F9%29=49sqrt%285%29%2F3 ALIGN=MIDDLE  ALT=\"%281%2F2%2914%2A21%28sqrt%285%29%2F9%29=49sqrt%285%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >= approx. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36.5 ALIGN=MIDDLE  ALT=\"36.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > square meters.<BR>\n" );
document.write( "The area of a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48.19%5Eo ALIGN=MIDDLE  ALT=\"48.19%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > wedge is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48.19%2F360 ALIGN=MIDDLE  ALT=\"48.19%2F360\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the area of the full circle., so the area of the XAB wedge, in square meters is about<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2848.19%2F360%29pi%2A21%5E2=about%2848.19%2F360%29%2A3.1416%2A441=185.5 ALIGN=MIDDLE  ALT=\"%2848.19%2F360%29pi%2A21%5E2=about%2848.19%2F360%29%2A3.1416%2A441=185.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Then, the total area the cow can graze, in square meters, is about<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36.5%2B185.5=222 ALIGN=MIDDLE  ALT=\"36.5%2B185.5=222\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "If the cow is outside that rectangular plot, and allowed to graze as far as the rope will allow;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C200%2C-45%2C27%2C-26%2C22%2C%0D%0Arectangle%280%2C0%2C-40%2C-14%29%2C%0D%0Aarc%280%2C0%2C42%2C42%2C-180%2C90%29%2C%0D%0Aarc%280%2C-14%2C14%2C14%2C90%2C180%29%2C%0D%0Agreen%28line%280%2C-14%2C0%2C-21%29%29%2Clocate%28-4%2C-6%2C14%29%2C%0D%0Alocate%28-4%2C-16%2Cgreen%287%29%29%2Clocate%28-11%2C4%2C21%29%2C%0D%0Ared%28circle%280%2C0%2C1%29%29%2Cred%28circle%28-21%2C0%2C1%29%29%2C%0D%0Ared%28circle%280%2C-21%2C1%29%29%2Cred%28circle%28-7%2C-14%2C1%29%29%2C%0D%0Alocate%281%2C2%2Cred%28X%29%29%2Clocate%28-22%2C-0.5%2Cred%28A%29%29%2C%0D%0Alocate%28-1%2C-22%2Cred%28B%29%29%2Clocate%28-9%2C-15%2Cred%28C%29%29%2C%0D%0Alocate%281.5%2C-12%2Cred%28Y%29%29%2Cred%28circle%280%2C-14%2C1%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > With the rope tight, a cow, tied at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28X%29 ALIGN=MIDDLE  ALT=\"red%28X%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , can circle from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28A%29 ALIGN=MIDDLE  ALT=\"red%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28B%29 ALIGN=MIDDLE  ALT=\"red%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and then to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28C%29 ALIGN=MIDDLE  ALT=\"red%28C%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The cow can graze on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F4 ALIGN=MIDDLE  ALT=\"3%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the 21-m radius circle centered at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28X%29 ALIGN=MIDDLE  ALT=\"red%28X%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and also on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F4 ALIGN=MIDDLE  ALT=\"1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" > of a 7-m radius circle centered at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28Y%29 ALIGN=MIDDLE  ALT=\"red%28Y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The total area, in square meters, is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F4%29%2Api%2A21%5E2%2B%281%2F4%29%2Api%2A7%5E2=%283%2F4%29%2Api%2A441%2B%281%2F4%29%2Api%2A49=%281323%2F4%29pi%2B%2849%2F4%29pi=%281372%2F4%29pi=highlight%28343pi%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is about <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1078 ALIGN=MIDDLE  ALT=\"1078\"   DISABLED_style= \"max-width:90%; height:auto;\" > square meters. </SPAN>\n" );
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