SOLUTION: PLEASE HELP how do i start to solve this problem? You have purchased a 42-inch television with an aspect ratio of 16:9. You want to watch a movie which has an aspect ratio of 1.8

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: PLEASE HELP how do i start to solve this problem? You have purchased a 42-inch television with an aspect ratio of 16:9. You want to watch a movie which has an aspect ratio of 1.8      Log On


   

Question 987761: PLEASE HELP how do i start to solve this problem?
You have purchased a 42-inch television with an aspect ratio of 16:9. You want to watch a movie which has an aspect ratio of 1.85:1. Find the following measurements
Height of the television screen
Width of the television screen
Height of the black bars at the top and bottom of the screen.
Percent of the area of the television screen that is covered by the image.
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
42-inch television has the aspect ratio of  16:9.

It means that  x%2Fy = 16%2F9,  where  x  and  y  are measures of the  TV screen in horizontal and vertical directions respectively,  in inches.

Hence,  x = 16%2F9y.       (1)

In addition,  by the Pythagorean theorem,  x%5E2 + y%5E2 = 42%5E2.

Substitute  (1)  here.  You will get

16%5E2%2F9%5E2%2Ay%5E2 + y%5E2 = 42%5E2,

256%2Ay%5E2 + 81%2Ay%5E2 = 42%5E2%2A81,

337%2Ay%5E2 = 142884,

y = sqrt%28142884%2F337%29 = 20.591 inches (approximately).

Hence,  x = 16%2F9y = 16%2F9.20.591 = 36.606 inches.

Now you know the dimensions of the TV set:  36.606 in  horizontally and  20.591 in  vertically.

This is how to start the solution.