How do I figure out dimensions of a rectangle, using proportions and a diagonal?

I have a geometry test on similarity tomorrow. So I was taking a practice quiz for lesson 8-2 on the Pearson Prentice Hall site, and couldn't figure out this question:



"In movies and television, the ratio of the width of the screen to the height is called the aspect ratio. Television screens usually have an aspect ratio of 4 : 3, while movie screens usually have an aspect ratio of 1.85 : 1. However, if a movie is made for television in "Letterbox" format, it retains the 1.85 : 1 aspect ratio and fills in the top and bottom parts of the screen with black bars. What would be the height of a movie in "Letterbox" format on a television screen that measures 25 inches along its diagonal? (Hint: First find the width and height of the television screen.)"



It says the answer is 10.81, but I had no idea how to arrive at the answer for the first step.How do I figure out dimensions of a rectangle, using proportions and a diagonal?
If you have a TV screen with a 25" diagonal, you have made a right triangle with the width and height as your two legs, and the diagonal as your hypotenuse. You don't know the width and height but you know that they are in a 4:3 ratio. How about saying the width is 4x and the height is 3x.



a^2 + b^2 = c^2

(4x)^2 + (3x)^2 = 25^2

16x^2 + 9x^2 = 625

25x^2 = 625

x^2 = 25

x = 5



so your TV width is 4x = 4*5 = 20 inches

your TV height is 3x = 3 * 5 = 15 inches



You know that the picture will fill the entire width of the TV screen, so you can set up a proportion



width on movie. . . .width on TV

----------------------- = ---------------------

height on movie. . .height on TV





1.85 . . . 20

------- = ---------

. 1 . . . . .h



1.85h = 20

h = 10.81



So the height of the move in letterbox would be 10.81 inches.