document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=779431>Question 779431</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving this word problem: A college is building a track in the shape of a rectangle with a semicircle at each end. The perimeter of the entire track is 200 pi feet and the area of only the rectangular region is 5000 pi square feet. Find the length and width of the rectangular region. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #475225 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=475225\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "rectangle with sides <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > with a semicircle at each end tells you that diameter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > of a semicircle is equal to the one side of the rectangle; let it be side <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then the radius of a semicircle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=b%2F2 ALIGN=MIDDLE  ALT=\"r=b%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The perimeter of the entire track is the perimeter of 2 semicircles  plus two sides of the rectangle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a+ ALIGN=MIDDLE  ALT=\"2a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > (we do not need diameters <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" > or sides <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >, they are inside a track).\r<BR>\n" );
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document.write( "since they are congruent, the perimeter of 2 semicircle equal to the perimeter of a circle which is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2rpi ALIGN=MIDDLE  ALT=\"2rpi\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28b%2F2%29pi=b%2Api ALIGN=MIDDLE  ALT=\"2%28b%2F2%29pi=b%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" > since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=b%2F2 ALIGN=MIDDLE  ALT=\"r=b%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=+2a%2Bb%2Api=200pi%2A+ft ALIGN=MIDDLE  ALT=\"P=+2a%2Bb%2Api=200pi%2A+ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >......equation 1\r<BR>\n" );
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document.write( "the area of only the rectangular region is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=ab=5000pi%2A+ft%5E2 ALIGN=MIDDLE  ALT=\"A=ab=5000pi%2A+ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >......equation 2\r<BR>\n" );
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document.write( "solve this system:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a%2Bb%2Api=200pi%2A+ft ALIGN=MIDDLE  ALT=\"2a%2Bb%2Api=200pi%2A+ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >......equation 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ab=5000%2Api%2A+ft%5E2 ALIGN=MIDDLE  ALT=\"ab=5000%2Api%2A+ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >......equation 2....solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%285000pi%29%2Fb ALIGN=MIDDLE  ALT=\"a=%285000pi%29%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" >......equation 2.....plug in equation 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%285000pi%29%2Fb%2Bb%2Api=200pi ALIGN=MIDDLE  ALT=\"2%285000pi%29%2Fb%2Bb%2Api=200pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >......equation 1...solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > and cancel <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810000%29%2Fb%2Bb+=200 ALIGN=MIDDLE  ALT=\"%2810000%29%2Fb%2Bb+=200\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....multiply by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28b%29%2810000%29%2Fcross%28b%29%2Bb%5E2=200b ALIGN=MIDDLE  ALT=\"cross%28b%29%2810000%29%2Fcross%28b%29%2Bb%5E2=200b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000%2Bb%5E2+-200b=0 ALIGN=MIDDLE  ALT=\"10000%2Bb%5E2+-200b=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-200b%2B10000=0 ALIGN=MIDDLE  ALT=\"b%5E2+-200b%2B10000=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28b+-100%29%5E2=0 ALIGN=MIDDLE  ALT=\"%28b+-100%29%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+-100=0 ALIGN=MIDDLE  ALT=\"b+-100=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=100ft ALIGN=MIDDLE  ALT=\"b+=100ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >..........now we know radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=50 ALIGN=MIDDLE  ALT=\"r=50\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the width of the rectangular region is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=100ft ALIGN=MIDDLE  ALT=\"b+=100ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "the length of the rectangular region will be\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=%285000pi%29%2F100 ALIGN=MIDDLE  ALT=\"a=%285000pi%29%2F100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=50pi%2Aft ALIGN=MIDDLE  ALT=\"a=50pi%2Aft\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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