ACT Math : How to find the length of the side of a pentagon

Study concepts, example questions & explanations for ACT Math

varsity tutors app store varsity tutors android store varsity tutors ibooks store

Example Questions

Example Question #13 : Geometry

The perimeter of a regular pentagon is \(\displaystyle 85\). What is the length of one side?

Possible Answers:

\(\displaystyle 8.5\)

\(\displaystyle 15\sqrt{3}\)

\(\displaystyle 14\sqrt{7}\)

\(\displaystyle 5\sqrt{6}\)

\(\displaystyle 17\)

Correct answer:

\(\displaystyle 17\)

Explanation:

A problem like this is very easy. A regular pentagon just looks like:

Pentagon

All of its sides are equal. Therefore, you know that \(\displaystyle 5s = 85\), where \(\displaystyle s\) is the length of one side. Solving for \(\displaystyle s\), you get \(\displaystyle s=17\).

Example Question #11 : Act Math

If the perimeter of a given regular pentagon is \(\displaystyle 1,268 \:in\). What is the length of one side of this regular pentagon in inches?

Possible Answers:

\(\displaystyle 254.4\)

\(\displaystyle 251.8\)

\(\displaystyle 248.8\)

\(\displaystyle 253.6\)

Correct answer:

\(\displaystyle 253.6\)

Explanation:

Use the formula for perimeter to solve for the side length of the regular pentagon:

\(\displaystyle P=5s\)

Where \(\displaystyle P\) is the perimeter and \(\displaystyle s\) is the length of a side.

In this case:

\(\displaystyle 1,268=5s\)

\(\displaystyle s=\frac{1,268}{5}=253.6\)

Example Question #1 : How To Find The Length Of The Side Of A Pentagon

Find the length of each side for regular pentagon with a perimeter of \(\displaystyle 55\).

Possible Answers:

\(\displaystyle 11.5\)

\(\displaystyle 12\)

\(\displaystyle 10.5\)

\(\displaystyle 11\)

Correct answer:

\(\displaystyle 11\)

Explanation:

Use the formula for perimeter to solve for the side length:

\(\displaystyle P=5s\)

\(\displaystyle 55=5s\)

\(\displaystyle s=11\)

Example Question #1 : How To Find The Length Of The Side Of A Pentagon

Find the length of one side for a regular pentagon with a perimeter of \(\displaystyle 115\).

Possible Answers:

\(\displaystyle 24\)

\(\displaystyle 22\)

\(\displaystyle 23\)

\(\displaystyle 21\)

Correct answer:

\(\displaystyle 23\)

Explanation:

Use the formula for perimeter to solve for the side length:

\(\displaystyle P=5s\)

\(\displaystyle 115=5s\)

\(\displaystyle s=23\)

Example Question #21 : Geometry

Find the length of each side for a regular pentagon with a perimeter of \(\displaystyle 14{,}000\).

Possible Answers:

\(\displaystyle 2{,}480\)

\(\displaystyle 2{,}900\)

\(\displaystyle 2{,}600\)

\(\displaystyle 2{,}800\)

Correct answer:

\(\displaystyle 2{,}800\)

Explanation:

Use the formula for perimeter to solve for the side length:

\(\displaystyle P=5s\)

\(\displaystyle 14,000=5s\)

\(\displaystyle s=2,800\)

Learning Tools by Varsity Tutors