Question

The figures below are similar. The labeled sides are corresponding.5 in6 inWhat is the ratio of the perimeter of the smaller pentagon to the perimeter of the larger pentagon?Write your answer as the ratio of two whole numbers separated by a colon (for example, 2:3).

Answer 1

The ratio of the perimeter of the smaller pentagon to the larger pentagon is 5:6

Step-by-step 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

`\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 = }(5)/(6) \\ \text{ ratio = 5 : 6} \end{gathered}`

Hence, the ratio of the perimeter of the smaller pentagon to the larger pentagon is 5:6