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 36 inches wide, and the DVD cover art is 4 inches wide. If the diagonal of the poster is 6.75 feet, what is the diagonal of the DVD cover art?

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

B. 8 inches

To find the scale factor, we need to divide the width of the poster by the width of the DVD cover art:

Scale factor = 36 inches / 4 inches = 9

Next, we can use the scale factor to find the diagonal of the DVD cover art:

Diagonal of DVD cover art = Scale factor * Diagonal of poster
Diagonal of DVD cover art = 9 * 6.75 feet = 60.75 feet

Convert 60.75 feet to inches:
60.75 feet * 12 inches/foot = 729 inches

Now we can use the Pythagorean theorem to find the diagonal of the DVD cover art:
diagonal^2 = width^2 + height^2
diagonal^2 = 4^2 + 36^2
diagonal^2 = 16 + 1296
diagonal^2 = 1312
diagonal = sqrt(1312)
diagonal ≈ 36.2 inches

Thus, the diagonal of the DVD cover art is approximately 36.2 inches, which is closest to 8 inches.

U sure?

Apologies for the error in my previous response. Let's correct the calculations:

Given:
Width of the poster = 36 inches
Width of the DVD cover art = 4 inches
Diagonal of the poster = 6.75 feet

First, let's calculate the scale factor:
Scale factor = Width of the DVD cover art / Width of the poster
Scale factor = 4 inches / 36 inches
Scale factor = 1/9

Now, let's calculate the diagonal of the DVD cover art:
Diagonal of the DVD cover art = Scale factor * Diagonal of the poster
Diagonal of the DVD cover art = (1/9) * 6.75 feet
Diagonal of the DVD cover art = 0.75 feet

Convert 0.75 feet to inches:
0.75 feet * 12 inches/foot = 9 inches

Therefore, the diagonal of the DVD cover art is 9 inches, which corresponds to option C.