SOLUTION: I have a picture of a outdoor running track The inside lane of the track will enclose an area that is the shape of a rectangle with a semicircle at each end. The length of the rec

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Question 13131: I have a picture of a outdoor running track
The inside lane of the track will enclose an area that is the shape of a rectangle with a semicircle at each end. The length of the rectanjular part of the track is 2W. The outdoor running track is 400 meters around the inside lane.
Each lane measures 1.25 meters in width. Find the perimeter of the outer edgeof the inside Lane?
Answer by glabow(165) About Me  (Show Source):
You can put this solution on YOUR website!
Consider the length of the track. It remains the same regardless of what the width of the lane is. So the only change is the length of the curve in the track (the semicircle). If the length of the track was 0, all that would be left is a circle with a diameter of d. The length (circumference) is PId.
Increasing the width of the track by 1.25 would increase the diameter of the dircle by 2.5. Now we have two equations:
c%5B1%5D=PI%28d%29 and c%5B2%5D=PI%28d%2B2.5%29 The difference between these two circumferences is the increase in the track length from the inside to the outside of the lane. That is: increase=PI%28d%2B2.5%29+-+PI%28d%29=PI%282.5%29
So the length of the track on the outside of the lane is 400%2B2.5%28PI%29