ANSWER
The ratio of the perimeter of the smaller pentagon to the larger pentagon is 5:6
EXPLANATION
Given that
The side length of the smaller pentagon is 5in
The side length of the larger pentagon is 6 in
Recall, that the perimeter of a pentagon is 5a
i.e., Perimeter of a pentagon = 5a
where a is the side length of the pentagon
For the smaller pentagon
The perimeter = 5 (5)
The perimeter = 25 in
For the larger perimeter
The perimeter = 5(6)
The perimeter = 30 in
Therefore, the ratio of the perimeter of the smaller pentagon to the larger pentagon can be calculated below as
[tex]\begin{gathered} \text{ ratio = }\frac{\text{ perimeter of the smaller pentagon}}{\text{ perimeter of the larger pentagon}} \\ \\ \text{ ratio = }\frac{\text{ 25}}{\text{ 30}} \\ \text{ } \\ \text{ ratio = }\frac{5}{6} \\ \text{ ratio = 5 : 6} \end{gathered}[/tex]Hence, the ratio of the perimeter of the smaller pentagon to the larger pentagon is 5:6