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In the racetrack shown above, regions I and III are semicircular with radius r. If region II is rectangular and its...

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by AAPL » Mon Nov 02, 2020 4:18 am

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2019-04-26_1746.png
In the racetrack shown above, regions I and III are semicircular with radius r. If region II is rectangular and its length is twice its width, what is the perimeter of the track in terms of r?

A. \(2r(\pi+2)\)
B. \(2r(\pi+4)\)
C. \(2r(\pi+8)\)
D. \(4r(\pi+2)\)
E. \(4r(\pi+4)\)

OA B
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Re: In the racetrack shown above, regions I and III are semicircular with radius r. If region II is rectangular and its.

by Scott@TargetTestPrep » Thu Nov 12, 2020 7:29 am
AAPL wrote: ↑
Mon Nov 02, 2020 4:18 am
 Official Guide

2019-04-26_1746.png

In the racetrack shown above, regions I and III are semicircular with radius r. If region II is rectangular and its length is twice its width, what is the perimeter of the track in terms of r?

A. \(2r(\pi+2)\)
B. \(2r(\pi+4)\)
C. \(2r(\pi+8)\)
D. \(4r(\pi+2)\)
E. \(4r(\pi+4)\)

OA B
Solution:

We see that the width of the rectangle = diameter of the semicircle = 2r, and the length of the rectangle = 4r.

The perimeter of the track consists of the circumference of one circle and twice the length of the rectangle in the middle. Therefore, the perimeter of the track is:

2πr + 2 x 4r2πr + 8r = 2r(π + 4)

Answer: B

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