SOLUTION: you are in charge of constructing a fence around the running track at a high school. the fence is to be built around the track so that there is a uniform gap between the outside ed
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Question 254881: you are in charge of constructing a fence around the running track at a high school. the fence is to be built around the track so that there is a uniform gap between the outside edge of the track and the fence.
a. what is the maximum width of the gap between the track and the fence if no more than 630 meters of fencing is used? (hint: use the equation for teh circumference of a circle.) two sides of the track are both 100m each the other two sides are both 81m each Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! the fence is to be built around the track so that there is a uniform gap between the outside edge of the track and the fence.
a. what is the maximum width of the gap between the track and the fence if no more than 630 meters of fencing is used?
two sides of the track are both 100m each. the other two sides are both 81m each
:
I assume this is an oval track with half circles on either end, 100 m apart
:
The circumference of the two half circles = 2(81) = 162 m
Find the diameter
pi * d = 162
d =
d = 51.566 meters
:
Subtract 200 m which run parallel to the straight sides of the track
630 - 200 = 430 m of fence available to enclose the two half circles
:
Let x = dist between the track and the fence
:
Find the diameter of the fence circle
pi * (51.566+2x) = 430
51.566 + 2x =
51.566 + 2x = 136.87
2x = 136.87 - 51.566
2x = 85.331
x =
x = 42.64 m dist from the track to the fence, all the way around
;
:
Check solution by finding the circumference
pi * (51.566 + 2(42.64)) = 429.9 ~ 430
