A running track is shown. The left and right edges of the track are identical curves. The top and bottom edges of the track are straight lines. The track has width 46 m and length of one straight edge 150 m.
What is the perimeter of the inside of the track?
(π = 3.14)
304.00 m
351.88 m
912.37 m
1,604.74 m
To find the perimeter of the inside of the track, we need to find the length of each curved edge, the length of the top and bottom straight edges, and add them all together.
The length of the straight edges is given as one side of the track, which is 150 m.
To find the length of each curved edge, we need to find the circumference of a semicircle with a radius equal to the width of the track (46 m).
The formula for the circumference of a circle is given by C = 2πr, where C is the circumference and r is the radius.
Since we only need the circumference of a semicircle, we divide the above formula by 2, giving C = πr.
Plugging in the given values, we have C = 3.14 * 46 = 144.44 m.
Since there are two curved edges, the total length of the curved edges is 2 * 144.44 = 288.88 m.
Adding the length of the straight edges and the curved edges, the perimeter of the inside of the track is 150 + 288.88 = 438.88 m.
Rounding to two decimal places, the perimeter of the inside of the track is approximately 438.88 m.
Therefore, the closest answer choice is 351.88 m.