First, let's find the scale factor between the poster and the DVD cover art.
Scale factor = width of DVD cover art / width of poster
Scale factor = 4 inches / 24 inches
Scale factor = 1/6
Next, let's find the height of the poster.
Using the Pythagorean theorem:
(24)^2 + h^2 = (4.5 feet)^2
576 + h^2 = 20.25
h^2 = 20.25 - 576
h^2 = 367.5625
h = √367.5625
h ≈ 19.17 feet
Now, let's find the height of the DVD cover art.
Height of DVD cover art = 1/6 * 19.17 feet
Height of DVD cover art ≈ 3.19 feet
Finally, let's find the diagonal of the DVD cover art using the Pythagorean theorem.
Diagonal of DVD cover art = √((4 inches)^2 + (3.19 feet)^2)
Diagonal of DVD cover art = √(16 + 10.1761)
Diagonal of DVD cover art = √26.1761
Diagonal of DVD cover art ≈ 5.12 feet
Therefore, the diagonal of the DVD cover art is approximately 5.12 feet.
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 24 inches wide, and the DVD cover art is 4 inches wide. If the diagonal of the poster is 4.5 feet, what is the diagonal of the DVD cover art?
3 answers
A.
0.75 inch
B.
8 inches
C.
9 inches
D.
6 inches
0.75 inch
B.
8 inches
C.
9 inches
D.
6 inches
Let's revise the solution:
Given:
Width of poster = 24 inches
Width of DVD cover art = 4 inches
Diagonal of poster = 4.5 feet
First, let's find the scale factor between the poster and the DVD cover art.
Scale factor = width of DVD cover art / width of poster
Scale factor = 4 inches / 24 inches
Scale factor = 1/6
Next, let's find the height of the poster.
Using the Pythagorean theorem:
(24)^2 + h^2 = (4.5 feet)^2
576 + h^2 = 20.25
h^2 = 20.25 - 576
h^2 = 555.75
h = √555.75
h ≈ 23.6 inches
Now, let's find the height of the DVD cover art.
Height of DVD cover art ≈ 1/6 * 23.6 inches
Height of DVD cover art ≈ 3.93 inches
Finally, let's find the diagonal of the DVD cover art using the Pythagorean theorem.
Diagonal of DVD cover art = √((4 inches)^2 + (3.93 inches)^2)
Diagonal of DVD cover art = √(16 + 15.4449)
Diagonal of DVD cover art = √31.4449
Diagonal of DVD cover art ≈ 5.61 inches
Therefore, the diagonal of the DVD cover art is approximately 5.61 inches. Therefore, the closest option among the given choices is B. 8 inches.
Given:
Width of poster = 24 inches
Width of DVD cover art = 4 inches
Diagonal of poster = 4.5 feet
First, let's find the scale factor between the poster and the DVD cover art.
Scale factor = width of DVD cover art / width of poster
Scale factor = 4 inches / 24 inches
Scale factor = 1/6
Next, let's find the height of the poster.
Using the Pythagorean theorem:
(24)^2 + h^2 = (4.5 feet)^2
576 + h^2 = 20.25
h^2 = 20.25 - 576
h^2 = 555.75
h = √555.75
h ≈ 23.6 inches
Now, let's find the height of the DVD cover art.
Height of DVD cover art ≈ 1/6 * 23.6 inches
Height of DVD cover art ≈ 3.93 inches
Finally, let's find the diagonal of the DVD cover art using the Pythagorean theorem.
Diagonal of DVD cover art = √((4 inches)^2 + (3.93 inches)^2)
Diagonal of DVD cover art = √(16 + 15.4449)
Diagonal of DVD cover art = √31.4449
Diagonal of DVD cover art ≈ 5.61 inches
Therefore, the diagonal of the DVD cover art is approximately 5.61 inches. Therefore, the closest option among the given choices is B. 8 inches.
4 answers