How to find the perimeter of a pentagon - SAT Math

Card 0 of 8

Question

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?

Answer

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

$d = 8 \cdot \frac{1}{6} = \frac{4}{3}$ miles.

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

$\frac{4}{3} \cdot 5,280 = 7,040$ feet.

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

$7,040 \div 264 = 26 \frac{2}{3}$ 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 $\frac{2}{3}$ of a sidelength, finishing closest to Point C.

Compare your answer with the correct one above

Question

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?

Answer

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

$d = 8 \cdot \frac{1}{6} = \frac{4}{3}$ miles.

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

$\frac{4}{3} \cdot 5,280 = 7,040$ feet.

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

$7,040 \div 264 = 26 \frac{2}{3}$ 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 $\frac{2}{3}$ of a sidelength, finishing closest to Point C.

Compare your answer with the correct one above

Question

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?

Answer

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

$d = 8 \cdot \frac{1}{6} = \frac{4}{3}$ miles.

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

$\frac{4}{3} \cdot 5,280 = 7,040$ feet.

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

$7,040 \div 264 = 26 \frac{2}{3}$ 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 $\frac{2}{3}$ of a sidelength, finishing closest to Point C.

Compare your answer with the correct one above

Question

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?

Answer

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

$d = 8 \cdot \frac{1}{6} = \frac{4}{3}$ miles.

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

$\frac{4}{3} \cdot 5,280 = 7,040$ feet.

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

$7,040 \div 264 = 26 \frac{2}{3}$ 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 $\frac{2}{3}$ of a sidelength, finishing closest to Point C.

Compare your answer with the correct one above

Question

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?

Answer

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

$d = 8 \cdot \frac{1}{6} = \frac{4}{3}$ miles.

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

$\frac{4}{3} \cdot 5,280 = 7,040$ feet.

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

$7,040 \div 264 = 26 \frac{2}{3}$ 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 $\frac{2}{3}$ of a sidelength, finishing closest to Point C.

Compare your answer with the correct one above

Question

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?

Answer

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

$d = 8 \cdot \frac{1}{6} = \frac{4}{3}$ miles.

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

$\frac{4}{3} \cdot 5,280 = 7,040$ feet.

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

$7,040 \div 264 = 26 \frac{2}{3}$ 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 $\frac{2}{3}$ of a sidelength, finishing closest to Point C.

Compare your answer with the correct one above

Question

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?

Answer

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

$d = 8 \cdot \frac{1}{6} = \frac{4}{3}$ miles.

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

$\frac{4}{3} \cdot 5,280 = 7,040$ feet.

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

$7,040 \div 264 = 26 \frac{2}{3}$ 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 $\frac{2}{3}$ of a sidelength, finishing closest to Point C.

Compare your answer with the correct one above

Question

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?

Answer

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

$d = 8 \cdot \frac{1}{6} = \frac{4}{3}$ miles.

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

$\frac{4}{3} \cdot 5,280 = 7,040$ feet.

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

$7,040 \div 264 = 26 \frac{2}{3}$ 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 $\frac{2}{3}$ of a sidelength, finishing closest to Point C.

Compare your answer with the correct one above

Tap the card to reveal the answer