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 hexagonal shelf, we first need to determine the perimeter of the smaller shelf.

Each side of the smaller shelf measures 5 inches, and since a hexagon has 6 sides, we can calculate the perimeter of the smaller shelf as follows:

\[ \text{Perimeter of smaller shelf} = \text{Side length} \times \text{Number of sides} = 5 \text{ inches} \times 6 = 30 \text{ inches} \]

Next, since the larger shelf is scaled up by a factor of 2, we first find the perimeter of the larger shelf by multiplying the perimeter of the smaller shelf by the scale factor:

\[ \text{Perimeter of larger shelf} = \text{Perimeter of smaller shelf} \times \text{Scale factor} = 30 \text{ inches} \times 2 = 60 \text{ inches} \]

Thus, the perimeter of the larger shelf is:

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