Question 104231: A fence is to be built around a track so that there is a uniform gap between the outside edge of the track and the fence. The Length of the straight portion of the track is 100 meters and the diameter of the curve is 81 meters. What is the Maximum width of the gap between the track and the fence if no more than 777 meters of fencing is used?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A fence is to be built around a track so that there is a uniform gap between the outside edge of the track and the fence. The Length of the straight portion of the track is 100 meters and the diameter of the curve is 81 meters. What is the Maximum width of the gap between the track and the fence if no more than 777 meters of fencing is used?
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Let x = width of the gap
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If you draw this out, it is apparent that 200 m of fencing will run parallel to
the straight portions of the track. Therefore, 777 - 200 = 577 ft is available
for the two half circles. The radius of the two half circles will be (x+81).
:
Use the circumference formula:
2 * pi * (x+81) = 577
6.2832x + 508.938 = 577
6.2832x = 577 - 508.938
6.2832x = 68.062
x = 68.062/6.2832
x = 10.83 ft is the width between the fence and the track
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Did this make sense? Any questions?
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