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”
1. Use the Pythagorean Theorem to calculate the height of each screen, and
complete the table.
2. Which screen is the largest that will fit on Yoselin’s shelf?
To find the height of each screen, we can use the Pythagorean Theorem, which states that for a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides (width and height).
For screen A:
Height = sqrt(diagonal^2 - width^2) = sqrt(15^2 - 13^2) = sqrt(225 - 169) = sqrt(56) ≈ 7.48 inches
For screen B:
Height = sqrt(diagonal^2 - width^2) = sqrt(22^2 - 19^2) = sqrt(484 - 361) = sqrt(123) ≈ 11.09 inches
For screen C:
Height = sqrt(diagonal^2 - width^2) = sqrt(32^2 - 28^2) = sqrt(1024 - 784) = sqrt(240) ≈ 15.49 inches
For screen D:
Height = sqrt(diagonal^2 - width^2) = sqrt(40^2 - 35^2) = sqrt(1600 - 1225) = sqrt(375) ≈ 19.36 inches
Now let's compare the height of each screen to the height of the shelf (17 inches) to determine the largest screen that will fit on Yoselin's shelf:
- Screen A: Height = 7.48 inches (fits on the shelf)
- Screen B: Height = 11.09 inches (fits on the shelf)
- Screen C: Height = 15.49 inches (does not fit on the shelf)
- Screen D: Height = 19.36 inches (does not fit on the shelf)
Therefore, the largest screen that will fit on Yoselin's shelf is Screen B.