Final answer:
To find the diagonal of the DVD cover art scaled from a movie poster, calculate the scale factor as 1/9 by dividing the width of the cover art by the width of the poster. Multiply the scale factor by the poster's diagonal to obtain the DVD cover art's diagonal, which is 8 inches.
Step-by-step explanation:
The question involves finding the diagonal of the DVD cover art given the diagonal and width of a movie poster that has been scaled down. Since the DVD cover art is a scaled-down version of the movie poster, we can use proportions to find the unknown diagonal.
We know that the width of the poster is 54 inches and the diagonal is 6 feet (72 inches).
First, we determine the scale factor by dividing the width of the DVD cover art by the width of the poster:
Scale factor = Width of DVD cover art / Width of poster
= 6 inches / 54 inches
= 1/9.
Since the DVD cover art is a scale image of the poster, the scale factor applies to the diagonal as well.
So we can find the diagonal of the DVD cover art by applying the same scale factor to the diagonal of the poster:
Diagonal of DVD cover art = Scale factor × Diagonal of poster
= 1/9 × 72 inches.
Diagonal of DVD cover art = 8 inches.
Therefore, the diagonal of the DVD cover art is 8 inches.