Question

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 54 inches wide, and the dvd cover art is 6 inches wide. if the diagonal of the poster is 6 feet, what is the diagonal of the dvd cover art?
a. 18 inches
b. 0.67 inch
c. 7 inches
d. 8 inches

Explanation:

Step1: Convert poster diagonal to inches

Since 1 foot = 12 inches, 6 feet = 6×12 = 72 inches.

Step2: Set up proportion

Let the diagonal of the DVD cover art be $x$ inches. The ratio of the widths is the same as the ratio of the diagonals. So $\frac{6}{54}=\frac{x}{72}$.

Step3: Solve the proportion

Cross - multiply: $54x=6\times72$. Then $54x = 432$. Divide both sides by 54: $x=\frac{432}{54}=8$ inches.

Answer:

D. 8 inches