SOLUTION: Comparing TVs The screen size of a television is determined by the length of the diagonal of the rectangular screen.Traditional TVs come in a 4 :3 format,meaning the ratio of the l

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Question 1207448: Comparing TVs The screen size of a television is determined by the length of the diagonal of the rectangular screen.Traditional TVs come in a 4 :3 format,meaning the ratio of the length to the width of the rectangular screen is 4 to 3.What is the area of a 50-inch traditional TV screen? What is the area of a 50-inch LCD TV whose screen is in a 16 :9 format? Which screen is larger?

I tried this one for 30 minutes and got no where. Help....
Answer by ikleyn(52760) About Me  (Show Source):
You can put this solution on YOUR website!
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Comparing TVs The screen size of a television is determined by the length of the diagonal
of the rectangular screen. Traditional TVs come in a 4 :3 format, meaning the ratio of the length
to the width of the rectangular screen is 4 to 3.
(a) What is the area of a 50-inch traditional TV screen?
(b) What is the area of a 50-inch LCD TV whose screen is in a 16 :9 format? Which screen is larger?
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(a)  Consider 4:3 format.

     It means that if W inches is the width, then the length is  L = %284%2F3%29W inches.


     Then the square of the diagonal is

          W%5E2 + L%5E2 = W%5E2 + %28%284%2F3%29W%29%5E2 = W%5E2+%2B+%2816%2F9%29W%5E2 = %281+%2B+16%2F9%29W%5E2 = %2825%2F9%29W%5E2  square inches.


     Thus  

          %2825%2F9%29W%5E2 = 50%5E2  square inches.


     It implies

          W%5E2 = %289%2F25%29%2A50%5E2 = %289%2F25%29%2A50%2A50 = 9%2A%2850%2F25%29%2A50 = 9*2*50 = 9*100 = 900.


     Hence,  W = sqrt%28900%29 = 30  inches.


     Thus the width is 30 inches, the length is  ((((4/3)*30}}} = 40 inches.


     So, this TV screen has dimensions 30 inches by 40 inches. 
     Its area is 30*40 = 1200 square inches.


     At this point, part (a) is solved, in full.



(b)  Solve (b) by the same (= the similar) way.