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?(1 point)

Question

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 is a hexagon, and since all sides are equal in a regular hexagon, we can use the following formula for the perimeter (P) of a hexagon:

\[ P = 6 \times \text{side length} \]

Given that the side length of the smaller shelf is 5 inches, we can calculate its perimeter:

\[ P_{\text{smaller}} = 6 \times 5 = 30 \text{ inches} \]

Now that we have the perimeter of the smaller shelf, we can find the perimeter of the larger shelf. Since Marco wants the larger shelf to be twice as big (meaning double the size), we can use the same scale factor for the perimeter. Thus, we multiply the perimeter of the smaller shelf by the scale factor (which is 2):

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

Therefore, the perimeter of the larger shelf is 60 inches.