Leo designs a piece of jewelry in the shape of a regular pentagon. Each side of the object measures 3 cm. Leo photographs the object, enlarges it so that the sides each measure 8 cm, and prints the photo. What scale factor did Leo use to create the photograph from the original?

Question

a. 2 1/3
b. 3/8
c. 2 2/3
c. 11

Answer 1

To find the scale factor Leo used to enlarge the original pentagon from 3 cm sides to 8 cm sides, we can use the formula for the scale factor:

\[ \text{Scale Factor} = \frac{\text{New Size}}{\text{Original Size}} \]

In this case, the new size is 8 cm (the size of the enlarged pentagon) and the original size is 3 cm (the size of the original pentagon). Plugging in these values, we get:

\[ \text{Scale Factor} = \frac{8 \text{ cm}}{3 \text{ cm}} = \frac{8}{3} \]

To convert this fraction into a mixed number, we divide 8 by 3:

\[ 8 \div 3 = 2 \quad \text{remainder} \quad 2 \]

This gives us:

\[ \frac{8}{3} = 2 \frac{2}{3} \]

Thus, the scale factor Leo used to create the photograph is \(2 \frac{2}{3}\).

So the correct answer is:

c. 2 2/3