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14. Find the perimeter (distance around) of the race track pictured below. The two vertical 30 yd long lines are not part of the track, they are just dimensions. 30 yds 80 yards

14. Find the perimeter (distance around) of the race track pictured below. The two vertical 30 yd long lines are not part of the track, they are just dimensions. 30 yds 80 yards

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Problem 14: Race Track Perimeter Calculation** **Task:** Determine the perimeter (distance around) of the illustrated race track. The diagram includes two vertical lines measuring 30 yards each, but these are not part of the track; they merely provide dimensions. **Description of the Diagram:** The diagram shows a race track in the shape of a rectangle with semi-circular ends. The dimensions are as follows: - The rectangle's length is labeled as 80 yards. - Each vertical segment outside the rectangle measures 30 yards and represents the diameter of the semi-circular ends of the track. **Explanation for Calculation:** 1. **Rectangle Part:** The length of the rectangle is 80 yards. 2. **Semi-circular Ends:** The diameter of each semi-circle is 30 yards, which implies the radius is 15 yards. The circumference of a full circle with this radius is \(2 \pi r = 30\pi\) yards. Since the track only includes half the circle at each end, the total for both is \(30\pi\) yards. **Perimeter Formula:** To find the perimeter, add the rectangular and curved sections: \[ \text{Perimeter} = 80 + \pi \times 30 \] This is the complete perimeter of the race track.
Transcribed Image Text:**Problem 14: Race Track Perimeter Calculation** **Task:** Determine the perimeter (distance around) of the illustrated race track. The diagram includes two vertical lines measuring 30 yards each, but these are not part of the track; they merely provide dimensions. **Description of the Diagram:** The diagram shows a race track in the shape of a rectangle with semi-circular ends. The dimensions are as follows: - The rectangle's length is labeled as 80 yards. - Each vertical segment outside the rectangle measures 30 yards and represents the diameter of the semi-circular ends of the track. **Explanation for Calculation:** 1. **Rectangle Part:** The length of the rectangle is 80 yards. 2. **Semi-circular Ends:** The diameter of each semi-circle is 30 yards, which implies the radius is 15 yards. The circumference of a full circle with this radius is \(2 \pi r = 30\pi\) yards. Since the track only includes half the circle at each end, the total for both is \(30\pi\) yards. **Perimeter Formula:** To find the perimeter, add the rectangular and curved sections: \[ \text{Perimeter} = 80 + \pi \times 30 \] This is the complete perimeter of the race track.
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