You can
put this solution on YOUR website! 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.
a = semi-major axis's length
2a = major axis's length = length of field
>>...the field must be between 135 and 185 meters long...<<
135 < 2a < 185
Divide through by 2
67.5 < a < 92.5
b = semi-minor axis's length
2b = minor axis's width = width of field
>>...the field must be...between 110 and 155 meters wide...<<
110 < 2b < 155
Divide through by 2:
55 < b < 77.5
a) write an equation for the largest allowable playing field.
The formula for the area of an ellipse is
Area = pab
The area is latgest when a and b are the largest, that is when
a = 92.5 and b = 77.5
Largest area = p(92.5)(77.5)
= 22521.3 mē approximately.
b) write an equation for the smallest allowable playing field.
The area is smallest when a and b are the smallest, that is when
a = 67.5 and b = 55
Smallest area = p(67.5)(55)
= 11663.2 mē approximately.
c) write an inequality that describes the possible areas of an Australian
football field.
11663.2 mē < Area < 22521.3 mē
Edwin
AnlytcPhil@aol.com
