document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1090034>Question 1090034</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the area of ellipse with an aspect ratio of two and total perimeter of 25 inches? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #704693 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=704693\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> what is the area of ellipse with an aspect ratio of two and total perimeter of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches? \r<BR>\n" );
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document.write( "For an ellipse, the aspect ratio denotes the ratio of the major axis <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >  to the minor axis <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   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 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;\" > are measured from the center, so they are like \"radius\" measures\r<BR>\n" );
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document.write( "given:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Fb=2 ALIGN=MIDDLE  ALT=\"a%2Fb=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2b ALIGN=MIDDLE  ALT=\"a=2b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and perimeter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=25 ALIGN=MIDDLE  ALT=\"P=25\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches\r<BR>\n" );
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document.write( "an approximation within about 5% of the true value, so long as a is not more than 3 times longer than b (in other words, the ellipse is not too \"squashed\"):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=2pi%2Asqrt%28%28a%5E2%2Bb%5E2%29%2F2%29 ALIGN=MIDDLE  ALT=\"P=2pi%2Asqrt%28%28a%5E2%2Bb%5E2%29%2F2%29\"   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=25=2pi%2Asqrt%28%28%282b%29%5E2%2Bb%5E2%29%2F2%29 ALIGN=MIDDLE  ALT=\"25=2pi%2Asqrt%28%28%282b%29%5E2%2Bb%5E2%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.............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;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+-%285+sqrt%285%2F2%29%29%2Fpi ALIGN=MIDDLE  ALT=\"b+=+-%285+sqrt%285%2F2%29%29%2Fpi\"   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+ ALIGN=MIDDLE  ALT=\"b+\"   DISABLED_style= \"max-width:90%; height:auto;\" >&#8776;  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2.51773699057992 ALIGN=MIDDLE  ALT=\"-2.51773699057992\"   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=2%2A%28-5sqrt%285%2F2%29%29%2Fpi+=+%28-10sqrt%285%2F2%29%29%2Fpi ALIGN=MIDDLE  ALT=\"a=2%2A%28-5sqrt%285%2F2%29%29%2Fpi+=+%28-10sqrt%285%2F2%29%29%2Fpi\"   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 ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > &#8776; <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-5.032921210448 ALIGN=MIDDLE  ALT=\"+-5.032921210448\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Ellipse area is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Area+=ab%2Api ALIGN=MIDDLE  ALT=\"Area+=ab%2Api\"   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=Area+=%28-10+sqrt%285%2F2%29%29%2Fpi%2A%28-5+sqrt%285%2F2%29%29%2Fpi%29%2Api ALIGN=MIDDLE  ALT=\"Area+=%28-10+sqrt%285%2F2%29%29%2Fpi%2A%28-5+sqrt%285%2F2%29%29%2Fpi%29%2Api\"   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=Area+=%28-10+sqrt%285%2F2%29%29%2Fpi%2A%28-5sqrt%285%2F2%29%29 ALIGN=MIDDLE  ALT=\"Area+=%28-10+sqrt%285%2F2%29%29%2Fpi%2A%28-5sqrt%285%2F2%29%29\"   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=Area+=125%2Fpi ALIGN=MIDDLE  ALT=\"Area+=125%2Fpi\"   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=Area=39.8 ALIGN=MIDDLE  ALT=\"Area=39.8\"   DISABLED_style= \"max-width:90%; height:auto;\" > in^2\r<BR>\n" );
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document.write( "check equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F%28%28-10+sqrt%285%2F2%29%29%2Fpi%29%5E2+%2B+y%5E2%2F%28+-%285+sqrt%285%2F2%29%29%2Fpi%29%5E2=1 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2F%28-5.032921210448%29%5E2+%2B+y%5E2%2F%28-2.51773699057992%29%5E2=1 ALIGN=MIDDLE  ALT=\"x%5E2%2F%28-5.032921210448%29%5E2+%2B+y%5E2%2F%28-2.51773699057992%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "it will give you:\r<BR>\n" );
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document.write( "area | <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=39.808917197 ALIGN=MIDDLE  ALT=\"39.808917197\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "perimeter | <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24.383816643 ALIGN=MIDDLE  ALT=\"24.383816643\"   DISABLED_style= \"max-width:90%; height:auto;\" >  which is an approximation  within about 5% of the true value\r<BR>\n" );
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