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”
1. Use the Pythagorean Theorem to calculate the height of each screen, and
complete the table. show your work
To calculate the height of each screen, we can use the Pythagorean theorem, which states that in 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^2 + Width^2 = Diagonal^2
Height^2 + 13^2 = 15^2
Height^2 + 169 = 225
Height^2 = 225 - 169
Height^2 = 56
Height = √56
Height ≈ 7.48 inches
For screen B:
Height^2 + Width^2 = Diagonal^2
Height^2 + 19^2 = 22^2
Height^2 + 361 = 484
Height^2 = 484 - 361
Height^2 = 123
Height = √123
Height ≈ 11.09 inches
For screen C:
Height^2 + Width^2 = Diagonal^2
Height^2 + 28^2 = 32^2
Height^2 + 784 = 1024
Height^2 = 1024 - 784
Height^2 = 240
Height = √240
Height ≈ 15.49 inches
For screen D:
Height^2 + Width^2 = Diagonal^2
Height^2 + 35^2 = 40^2
Height^2 + 1225 = 1600
Height^2 = 1600 - 1225
Height^2 = 375
Height = √375
Height ≈ 19.36 inches
The completed table is:
Screen Diagonal Width Height
A 15” 13” 7.48”
B 22” 19” 11.09”
C 32” 28” 15.49”
D 40” 35” 19.36”