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.
Screen Diagonal Width Height
A 15” 13” 9.75”
B 22” 19” 14.25”
C 32” 28” 21”
D 40” 35” 26.25”
To use the Pythagorean Theorem to calculate the height of each screen, we can use the formula:
height^2 = diagonal^2 - width^2
Let's calculate the height for each screen:
For Screen A:
height^2 = 15^2 - 13^2
height^2 = 225 - 169
height^2 = 56
height = √56
height ≈ 7.48 inches
For Screen B:
height^2 = 22^2 - 19^2
height^2 = 484 - 361
height^2 = 123
height = √123
height ≈ 11.09 inches
For Screen C:
height^2 = 32^2 - 28^2
height^2 = 1024 - 784
height^2 = 240
height = √240
height ≈ 15.49 inches
For Screen D:
height^2 = 40^2 - 35^2
height^2 = 1600 - 1225
height^2 = 375
height = √375
height ≈ 19.36 inches
Now that we have calculated the height for each screen, we can complete the table:
Screen | Diagonal | Width | Height
----------------------------------
A | 15” | 13” | 7.48”
B | 22” | 19” | 11.09”
C | 32” | 28” | 15.49”
D | 40” | 35” | 19.36”
To calculate the height of each screen, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
Let's calculate the height for each screen using this theorem:
Screen A:
The diagonal is 15 inches, and the width is 13 inches. Using the Pythagorean theorem, we can calculate the height:
height^2 = diagonal^2 - width^2
height^2 = 15^2 - 13^2
height^2 = 225 - 169
height^2 = 56
height = √56
height ≈ 7.48 inches
Screen B:
The diagonal is 22 inches, and the width is 19 inches. Using the Pythagorean theorem, we can calculate the height:
height^2 = diagonal^2 - width^2
height^2 = 22^2 - 19^2
height^2 = 484 - 361
height^2 = 123
height = √123
height ≈ 11.09 inches
Screen C:
The diagonal is 32 inches, and the width is 28 inches. Using the Pythagorean theorem, we can calculate the height:
height^2 = diagonal^2 - width^2
height^2 = 32^2 - 28^2
height^2 = 1024 - 784
height^2 = 240
height = √240
height ≈ 15.49 inches
Screen D:
The diagonal is 40 inches, and the width is 35 inches. Using the Pythagorean theorem, we can calculate the height:
height^2 = diagonal^2 - width^2
height^2 = 40^2 - 35^2
height^2 = 1600 - 1225
height^2 = 375
height = √375
height ≈ 19.36 inches
Completing the table, we have:
Screen A:
Diagonal: 15"
Width: 13"
Height: 7.48"
Screen B:
Diagonal: 22"
Width: 19"
Height: 11.09"
Screen C:
Diagonal: 32"
Width: 28"
Height: 15.49"
Screen D:
Diagonal: 40"
Width: 35"
Height: 19.36"
using that info, 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 compare the height of each screen to the height of the shelf (17 inches).
Based on the calculations we made earlier, the heights of the screens are as follows:
Screen A: 7.48 inches
Screen B: 11.09 inches
Screen C: 15.49 inches
Screen D: 19.36 inches
Since the shelf is 17 inches tall, the screen that will fit on the shelf is the one with a height less than or equal to 17 inches.
Therefore, the largest screen that will fit on Yoselin's shelf is Screen C, with a height of 15.49 inches.