Question

A pentagon train is made by attaching regular pentagons with 1" sides so that each pentagon, except the two on the ends, is attached to exactly two other pentagons along sides, as shown. How many inches are in the perimeter of a pentagon train made from 85 pentagons?

Answer 1

There are 341 inches from the perimeter of a pentagon train made from 85 pentagons

Explanation:

A pentagon is a polygon with five sides. A regular pentagon have all the five sides equal in length and also all the five interior angles equal.

The perimeter of a pentagon = 5l

Nof for a pentagon train attached to 1 pentagon by its sides;

The perimeter = (5 × 1 - (1-1))

Perimeter = 5

For pentagon train attached to two pentagon

Perimeter = ( 5×2 - (2-1))

Perimeter = (10 1)

Perimeter = 9

For pentagon train with n pentagon

Perimeter = ( 5× n -(n-1))

Perimeter = 5n - n+1

Perimeter = 4n + 1

∴ For pentagon train attached to 85 pentagon; where n=85

Perimeter = 4 n + 1

Perimeter = (4 × 85)+1

Perimeter = 340+1

Perimeter = 341 inches

There are 341 inches from the perimeter of a pentagon train made from 85 pentagons