document.write( "Question 40291: Australian football is played on an elliptical field. The official rules state that the field must be between 135 and 185 meters long and between 110 and 155 meters wide.\r
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Algebra.Com's Answer #25646 by AnlytcPhil(1806)\"\" \"About 
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Australian football is played on an elliptical field. The official rules state\r\n" );
document.write( "that the field must be between 135 and 185 meters long and between 110 and 155\r\n" );
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document.write( "a = semi-major axis's length\r\n" );
document.write( "2a = major axis's length = length of field\r\n" );
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document.write( ">>...the field must be between 135 and 185 meters long...<<\r\n" );
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document.write( "                135 < 2a < 185\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "               67.5 < a < 92.5 \r\n" );
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document.write( "b = semi-minor axis's length\r\n" );
document.write( "2b = minor axis's width = width of field\r\n" );
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document.write( ">>...the field must be...between 110 and 155 meters wide...<<\r\n" );
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document.write( "                110 < 2b < 155\r\n" );
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document.write( "Divide through by 2:\r\n" );
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document.write( "                 55 < b < 77.5 \r\n" );
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document.write( "a) write an equation for the largest allowable playing field.\r\n" );
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document.write( "The formula for the area of an ellipse is \r\n" );
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document.write( "                   Area = pab \r\n" );
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document.write( "The area is latgest when a and b are the largest, that is when\r\n" );
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document.write( "              a = 92.5 and b = 77.5 \r\n" );
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document.write( "          Largest area = p(92.5)(77.5)\r\n" );
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document.write( "                       = 22521.3 mē approximately. \r\n" );
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document.write( "b) write an equation for the smallest allowable playing field.\r\n" );
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document.write( "The area is smallest when a and b are the smallest, that is when\r\n" );
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document.write( "              a = 67.5 and b = 55 \r\n" );
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document.write( "         Smallest area = p(67.5)(55)\r\n" );
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document.write( "                       = 11663.2 mē approximately.\r\n" );
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document.write( "c) write an inequality that describes the possible areas of an Australian\r\n" );
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document.write( "                 11663.2 mē < Area <  22521.3 mē\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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