Final answer:
To find the approximate perimeter of the track, you need to calculate the perimeter of the rectangular part and the circumference of each semi-circle, then add them together. The perimeter of the rectangular part can be found using the formula 2(length + width). The circumference of a semi-circle is given by the formula π * radius.
Step-by-step explanation:
The track consists of a rectangular area and two semi-circular areas. The area of the rectangular part of the track is 32,000 square yards and the length of the shorter side of the track is 160 yards. In order to find the approximate perimeter of the entire track, we need to find the circumference of the two semi-circles and the perimeter of the rectangular part and add them together.
The perimeter of a rectangle is given by the formula: Perimeter = 2(length + width). Since the length and width of the rectangular part are not given, we need to find the missing dimension first. Since the area of the rectangular part is 32,000 square yards and one side is 160 yards, we can divide the area by the given side length to get the missing dimension: 32,000 / 160 = 200 yards. Now we can calculate the perimeter of the rectangular part as: Perimeter = 2(160 + 200) = 720 yards.
The circumference of a semi-circle is given by the formula: Circumference = π * radius. We know that the length of the shorter side of the track is the diameter of the semi-circles, so the radius is half of the diameter, which is 160 / 2 = 80 yards. Therefore, the circumference of each semi-circle is: Circumference = 3.14 * 80 = 251.2 yards. Since there are two semi-circles, we need to multiply this by 2.
Finally, we can calculate the approximate perimeter of the track by adding the perimeters of the rectangular part and the two semi-circular parts: Perimeter = 720 + 2(251.2) = 1222.4 yards.