Marco is building two wooden shelves that resemble a hexagon. He wants the bigger shelf to be twice as big as the smaller shelf, so he uses a scale factor of 2. What is the perimeter of the larger shelf if the smaller shelf has sides that measure 5 inches?

Answer 1

To find the perimeter of the larger shelf, we first need to calculate the perimeter of the smaller shelf.

The smaller shelf resembles a hexagon, which has 6 sides. Each side measures 5 inches. Therefore, the perimeter \( P \) of the smaller hexagonal shelf can be calculated as follows:

\[ P_{\text{smaller}} = \text{number of sides} \times \text{length of each side} \] \[ P_{\text{smaller}} = 6 \times 5 , \text{inches} = 30 , \text{inches} \]

Now that we have the perimeter of the smaller shelf, we know that the larger shelf is supposed to be twice as large. To find the perimeter of the larger shelf, we multiply the perimeter of the smaller shelf by the scale factor, which is 2:

\[ P_{\text{larger}} = \text{scale factor} \times P_{\text{smaller}} \] \[ P_{\text{larger}} = 2 \times 30 , \text{inches} = 60 , \text{inches} \]

Thus, the perimeter of the larger shelf is:

\[ \boxed{60} \text{ inches} \]