Screen Size
Computer screens and television screens are usually measured by the diagonal of
the screen. For example, a screen of size 60 inches would have a diagonal of 60
inches, a width of 52 inches, and a height of 30 inches.
Yoselin would like to install a new screen on a shelf that is 17 inches tall and 50
inches wide. She would like the screen to be the largest size that will fit on the
shelf. She knows the diagonal and width of the 4 screens listed below.
Screen Diagonal Width Height
A 15” 13”
B 22” 19”
C 32” 28”
D 40” 35”
2. Which screen is the largest that will fit on Yoselin’s shelf?
To determine which screen is the largest that will fit on Yoselin's shelf, we need to calculate the height of each screen using the given width and diagonal measurements.
For screen A:
Using the Pythagorean theorem, we can find the height:
height^2 = diagonal^2 - width^2
height^2 = 15^2 - 13^2
height^2 = 225 - 169
height^2 = 56
height = sqrt(56) ≈ 7.48 inches
For screen B:
height^2 = 22^2 - 19^2
height^2 = 484 - 361
height^2 = 123
height = sqrt(123) ≈ 11.09 inches
For screen C:
height^2 = 32^2 - 28^2
height^2 = 1024 - 784
height^2 = 240
height = sqrt(240) ≈ 15.49 inches
For screen D:
height^2 = 40^2 - 35^2
height^2 = 1600 - 1225
height^2 = 375
height = sqrt(375) ≈ 19.36 inches
Now we can compare the heights and select the largest screen that will fit on Yoselin's shelf:
- Screen A has a height of 7.48 inches, which is smaller than the shelf's height of 17 inches.
- Screen B has a height of 11.09 inches, which is also smaller than the shelf's height.
- Screen C has a height of 15.49 inches, which is still smaller than the shelf's height.
- Screen D has a height of 19.36 inches, which is larger than the shelf's height.
Therefore, the largest screen that will fit on Yoselin's shelf is screen D with a diagonal of 40 inches.