SOLUTION: an athletic field is a rectangle, 120 yd by 60 yd. with a semicircle at each of the ends. a running track 15yd wide surrounds the field. how many yards of fencing do you need to su
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Question 556813: an athletic field is a rectangle, 120 yd by 60 yd. with a semicircle at each of the ends. a running track 15yd wide surrounds the field. how many yards of fencing do you need to surround the outside edge of the track? round your answer to the nearest tenth of a yard. use 3.14 for PI Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! the track is a rectangle 120 yards by 60 yards with a semi-circle at each of the ends.
running track is 15 yards wide.
outside perimeter of the track is equal to what?
along the length of the field, the outside edge will be 120 yards long on each side for a total of 120 yards.
the circular part of the track will have a large radius of 45 yards which will give it a perimeter along the outside of the track of 45*pi = 45*3.14 = 141.3 yards.
the total perimeter of the track will be 2 * 120 + 2 * 141.3 = 240 + 282.6 = 522.6 yards.
a picture of your track is shown below:
the top picture shows the rectangular field and the outside and inside edge of the track.
the bottom picture shows the outside edge of the rectangular field plus the track only.
the length of the outside edge of the rectangular field is 120 + 120 = 240 yards.
the length of the outside edge of the circular part of the field is 141.3 + 141.3 = 282.6 yards.
the total outside edge is 240 + 282.6 = 522.6 yards.
that's how much fence you need.
each outside edge of the field is equal to 1/2 the perimeter of a circle.
put those 2 halves together and you get the perimeter of a circle.
the formula for the perimeter of a circle is 2 * pi * r.
the radius of the circle is equal to 1/2 the width of the original field plus 15 = 45 yards.
