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 x
2 + y
2 = 71
2.
Substitute x = 7y / 3 into the Pythagorean Theorem to get:
(7y/3)
2 + y
2 = 71
2
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 x
2 + y
2 = 71
2.
Substitute x = 2.35y into the Pythagorean Theorem to get:
(2.35y)
2 + y
2 = 71
2
Solving, you get y = 27.8" and then x = 65.33".