document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=254881>Question 254881</A>: <I><SPAN STYLE=\"word-break: break-all;\"> you are in charge of constructing a fence around the running track at a high school. the fence is to be built around the track so that there is a uniform gap between the outside edge of the track and the fence.<BR>\n" );
document.write( "a. what is the maximum width of the gap between the track and the fence if no more than 630 meters of fencing is used? (hint: use the equation for teh circumference of a circle.) two sides of the track are both 100m each the other two sides are both 81m each </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #187287 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=187287\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  the fence is to be built around the track so that there is a uniform gap between the outside edge of the track and the fence.<BR>\n" );
document.write( "a. what is the maximum width of the gap between the track and the fence if no more than 630 meters of fencing is used?<BR>\n" );
document.write( "two sides of the track are both 100m each. the other two sides are both 81m each<BR>\n" );
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document.write( "I assume this is an oval track with half circles on either end, 100 m apart<BR>\n" );
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document.write( "The circumference of the two half circles = 2(81) = 162 m<BR>\n" );
document.write( "Find the diameter<BR>\n" );
document.write( "pi * d = 162<BR>\n" );
document.write( "d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=162%2Fpi ALIGN=MIDDLE  ALT=\"162%2Fpi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d = 51.566 meters<BR>\n" );
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document.write( "Subtract 200 m which run parallel to the straight sides of the track<BR>\n" );
document.write( "630 - 200 = 430 m of fence available to enclose the two half circles<BR>\n" );
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document.write( "Let x = dist between the track and the fence<BR>\n" );
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document.write( "Find the diameter of the fence circle<BR>\n" );
document.write( "pi * (51.566+2x) = 430<BR>\n" );
document.write( "51.566 + 2x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=430%2Fpi ALIGN=MIDDLE  ALT=\"430%2Fpi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "51.566 + 2x = 136.87<BR>\n" );
document.write( "2x = 136.87 - 51.566<BR>\n" );
document.write( "2x = 85.331<BR>\n" );
document.write( "x = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=85.31%2F2 ALIGN=MIDDLE  ALT=\"85.31%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "x = 42.64 m dist from the track to the fence, all the way around<BR>\n" );
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document.write( "Check solution by finding the circumference<BR>\n" );
document.write( "pi * (51.566 + 2(42.64)) = 429.9 ~ 430<BR>\n" );
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