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 feet, what is the diagonal of the DVD cover art?
To find the scale factor between the poster and the DVD cover art, we can use the ratio of their widths:
Scale Factor = DVD cover art width / Poster width = 4 inches / 36 inches = 1/9
Next, we can find the height of the poster using the scale factor:
Poster height = Scale factor * DVD cover art height = (1/9) * (6 feet * 12 inches/feet) = 8 inches
Now, we can find the diagonal of the DVD cover art using the Pythagorean theorem:
Diagonal^2 = width^2 + height^2
Diagonal^2 = 4^2 + 8^2
Diagonal^2 = 16 + 64
Diagonal^2 = 80
Diagonal = √80 ≈ 8.94 inches
Therefore, the diagonal of the DVD cover art is approximately 8.94 inches.