The image on a movie poster was shrunk to make the DVD cover art for the movie, so that the cover art is a scale image of the poster. The poster is 30 inches wide, and the DVD cover art is 5 inches wide. If the diagonal of the poster is 4.5 feet, what is the diagonal of the DVD cover art?

A.
8 inches
B.
0.75 inch
C.
7.5 inches
D.
9 inches

1 answer

To solve for the diagonal of the DVD cover art, we first need to determine the scale factor by which the movie poster is reduced to create the DVD cover art.

The width of the poster is 30 inches, and the width of the DVD cover art is 5 inches. The scale from the poster to the DVD cover art can be calculated as follows:

\[ \text{Scale factor} = \frac{\text{Width of DVD cover art}}{\text{Width of poster}} = \frac{5 \text{ inches}}{30 \text{ inches}} = \frac{1}{6} \]

Now, we also know the diagonal of the poster is 4.5 feet. Since we want all our measurements in inches, we convert the diagonal from feet to inches:

\[ 4.5 \text{ feet} = 4.5 \times 12 \text{ inches} = 54 \text{ inches} \]

Next, we will apply the same scale factor to the diagonal of the poster to find the diagonal of the DVD cover art:

\[ \text{Diagonal of DVD cover art} = \text{Diagonal of poster} \times \text{Scale factor} = 54 \text{ inches} \times \frac{1}{6} \]

Now we calculate the result:

\[ \text{Diagonal of DVD cover art} = 54 \div 6 = 9 \text{ inches} \]

Thus, the diagonal of the DVD cover art is:

\[ \boxed{9 \text{ inches}} \]

Which corresponds to option D.