Question

The figures below are similar. The labeled sides are corresponding.2 yd5 ydWhat is the ratio of the perimeter of the smaller hexagon to the perimeter of the larger hexagon?Write your answer as the ratio of two whole numbers separated by a colon (for example, 2:3).

Answer 1

The perimeter of a regular hexagon is calculated using the formula:

`P=6l`

where l is the length of a side of the hexagon.

The perimeter of the small hexagon is given to be:

`\begin{gathered} l=2 \\ \therefore \\ P=6(2)=12 \end{gathered}`

The perimeter of the big hexagon is given to be:

`\begin{gathered} l=5 \\ \therefore \\ P=6(5)=30 \end{gathered}`

Therefore, the ratio will be:

`12:30`

We can simplify the ratio by dividing through by 6.

Therefore, the ratio is:

`2:5`