How to find the length of the side of a pentagon

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SAT Math › How to find the length of the side of a pentagon

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Pentagon

The above diagram shows a pentagonal track with perimeter one third of a mile. Adrianne starts at Point A and runs clockwise until she gets halfway between Points D and E. Which of the following choices is closest to the number of feet she runs?

1,200 feet

1,300 feet

1,100 feet

1,400 feet

1,000 feet

Explanation

The perimeter of the pentagonal track is one third of a mile; one mile is equal to 5,280 feet, so the perimeter is

$\frac{1}{3} \times 5, 280 = 1,760$ feet.

Each side of the pentagon has length one fifth of its perimeter, or

$\frac{1}{5} \times 1,760 = 352$ feet.

Adrianne runs three and one half sides, or

$3 \frac{1}{2} \times 352 = 1,232$ feet.

This makes 1,200 feet the closest, and correct, choice.

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