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.
To use the Pythagorean Theorem, we need to know the width and height of each screen. However, the only measurements given in the table are the diagonal and width. We can use these measurements to find the height using the Pythagorean Theorem.
According to the theorem, the square of the diagonal is equal to the sum of the squares of the width and height.
For Screen A:
Diagonal^2 = Width^2 + Height^2
15^2 = 13^2 + Height^2
225 = 169 + Height^2
Height^2 = 56
Height ≈ √56 ≈ 7.48
For Screen B:
Diagonal^2 = Width^2 + Height^2
22^2 = 19^2 + Height^2
484 = 361 + Height^2
Height^2 = 123
Height ≈ √123 ≈ 11.09
For Screen C:
Diagonal^2 = Width^2 + Height^2
32^2 = 28^2 + Height^2
1024 = 784 + Height^2
Height^2 = 240
Height ≈ √240 ≈ 15.49
For Screen D:
Diagonal^2 = Width^2 + Height^2
40^2 = 35^2 + Height^2
1600 = 1225 + Height^2
Height^2 = 375
Height ≈ √375 ≈ 19.36
The completed table with the calculated heights of each screen is as follows:
Screen | Diagonal | Width | Height
A | 15" | 13" | 7.48"
B | 22" | 19" | 11.09"
C | 32" | 28" | 15.49"
D | 40" | 35" | 19.36"