Question

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 four screens listed below.

Screen
Diagonal
Width
Height
A
15"
13"

B
22"
19"

C
32"
28"

D
40"
35"
Use the Pythagorean Theorem to calculate the height of each screen.
Which screen is the largest that will fit on Yoselin’s shelf?

Answer 1

To calculate the height of each screen, we can use the Pythagorean Theorem, which states that the square of the hypotenuse (diagonal) of a right triangle is equal to the sum of the squares of the other two sides.

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 see which screen will fit on Yoselin's shelf.
Screen A has a height of 7.48 inches, which is smaller than the shelf height of 17 inches.
Screen B has a height of 11.09 inches, which is also smaller than the shelf height.
Screen C has a height of 15.49 inches, which is smaller than the shelf height.
Screen D has a height of 19.36 inches, which is greater than the shelf height.

Therefore, the largest screen that will fit on Yoselin's shelf is screen D, with a diagonal of 40 inches, a width of 35 inches, and a height of approximately 19.36 inches.