SAT Math : How to find the perimeter of a pentagon

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : Pentagons

Pentagon

Aristotle High School has an unusual track in that it is shaped like a regular pentagon. Each side of the pentagon measures 264 feet.

Benny runs at a steady speed of eight miles an hour for ten minutes, starting at point A and working his way clockwise. When he is finished, which of the following points is he closest to?

Possible Answers:

Point A

Point B

Point E

Point C

Point D

Correct answer:

Point C

Explanation:

Benny runs at a rate of eight miles an hour for ten minutes, or \(\displaystyle \frac{10}{60} = \frac{1}{6}\) hours. The distance he runs is equal to his rate multiplied by his time, so, setting\(\displaystyle r = 8 , t = \frac{1}{6}\) in this formula:

\(\displaystyle d = rt\)

\(\displaystyle d = 8 \cdot \frac{1}{6} = \frac{4}{3}\) miles.

One mile comprises 5,280 feet, so this is equal to 

\(\displaystyle \frac{4}{3} \cdot 5,280 = 7,040\) feet.

Since each side of the track measures 264 feet, this means that Benny runs 

\(\displaystyle 7,040 \div 264 = 26 \frac{2}{3}\) sidelengths.

This means Benny runs around the track for 25 sidelengths, which is 5 complete times, back to Point A; he then runs one more complete sidelength to Point B; and, finally, he runs \(\displaystyle \frac{2}{3}\) of a sidelength, finishing closest to Point C.

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