Question

A group of friends is walking around a tract that is shaped like a regular pentagon. Each side measures 85 metres. If they make 3 complete trips around the track, how far will they have walked?

Answer 1

Hint: Here in this question, we have to find the distance walked by a group of friends. Given a track shaped like a regular pentagon so first, we need to find the perimeter of a regular pentagon of given length $$l$$ using a formula $$P=5\times l$$. And further multiply the resultant perimeter with the number of complete trips around the track walked by a group of friends. Simplify using the multiplication operation to get the required solution.

Complete step by step solution:
In geometry, perimeter can be defined as the path or the boundary that surrounds a shape. It can also be defined as the length of the outline of a shape.
If a pentagon is regular, then all the sides are equal in length, and five angles are of equal measures
Consider a given question:
A group of friends is walking around a tract that is shaped like a regular pentagon having each side measures 85 m and they complete 3 trips around the track. We need to find the total distance walked by a group of friends.
Given track means regular pentagon having length of $$85m$$, which is same for all sides of pentagon
First, find the perimeter or the distance around the track to complete a one trip. For a regular pentagon, the perimeter is the sum of the five sides or the length $$85m$$ of a side multiplied by five i.e.,
$$\Rightarrow P=5\times 85$$
On multiplication, we get
$$\therefore P=425$$meters.
Hence, the distance around the track to complete a one trip is $$425m$$
Now, find the distance to complete a 3 trip around a track is:
$$\Rightarrow d=3\times 425$$
On multiplication, we get
$$\therefore d=1275$$meters.
Therefore, the group of friends walked $$1275$$ meters or $$1.275km$$.

Note: Remember in any regular polygons all sides are of equal length and all angles between the two sides are also equal measures. While doing measurement based problems, do not forget to write the unit with the final answer, the unit for the perimeter will be the same as the unit of the length of a side or polygon.