High Definition TVs have screens in the ratio of 16:9. This year, Vizio plans to introduce Ultra-High Definition TV
screens with a ratio of 21:9, in three sizes: 50-inch, 58-inch, and 71-inch screens (TV screens are measured diagonally).
Find the dimensions of a 71-inch screen in Vizio's new Ultra-High Definition aspect ratio of 21:9.
Many movies have an aspect ratio of 2.35 : 1. Compare this with the HD ratio of 16:9 (or 1.77 : 1) and
the UHD ratio of 21 : 9 (or 2.33 : 1). Now find the dimensions of a movie on a 71-inch TV screen.
Solution to the Problem:
The dimensions of the Ultra-High Definition 71-inch TV screen are 65.26" x 27.97".The dimensions of a movie on a 71-inch TV screen are 65.33" x 27.8",
so the movie will fit almost exactly on the new Ultra-High Def screen
(so you won't see those black bars above and below the image like you do on a 16:9 screen).
Let x = horizontal dimension and let y = vertical component.
Then x/y = 21/9, so x = 7y / 3.
Then use the Pythagorean Theorem to get x2 + y2 = 712.
Substitute x = 7y / 3 into the Pythagorean Theorem to get:
(7y/3)2 + y2 = 712
Solving, you get y = 27.97" and then x = 65.26".
In a similar manner, let x = horizontal component and let y = vertical component of the movie.
Then x/y = 2.35, so x = 2.35y.
Then use the Pythagorean Theorem to get x2 + y2 = 712.
Substitute x = 2.35y into the Pythagorean Theorem to get:
(2.35y)2 + y2 = 712
Solving, you get y = 27.8" and then x = 65.33".
Correctly solved by:
| 1. James Alarie | Flint, Michigan |
| 2. David and Judy Dixon | Bennettsville, South Carolina |