SOLUTION: when tom arrives at the tv store, he learns that screen sizes are measured diagonally in inches and that the length and widths of the screens are always a ratio of 16:9 if the b

Algebra ->  Pythagorean-theorem -> SOLUTION: when tom arrives at the tv store, he learns that screen sizes are measured diagonally in inches and that the length and widths of the screens are always a ratio of 16:9 if the b      Log On


   

Question 1020876: when tom arrives at the tv store, he learns that screen sizes are measured diagonally in inches and that the length and widths of the screens are always a ratio of 16:9
if the biggest plasma screen tv ever produced was 150". how long and wide was it?
Answer by ikleyn(52781) About Me  (Show Source):
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When tom arrives at the tv store, he learns that screen sizes are measured diagonally in inches and that the length and widths of the screens are always a ratio of 16:9.
If the biggest plasma screen tv ever produced was 150", how long and wide was it?
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x%2Fy = 16%2F9,            (1)

sqrt%28x%5E2+%2B+y%5E2%29 = 150.   (2)


From (1) x = %2816%2F9%29%2Ay. Substitute it into (2). You will get

sqrt%28%2816%2F9%29%5E2%2Ay%5E2+%2B+y%5E2%29 = 150,   or

sqrt%28256y%5E2+%2B+81%2Ay%5E2%29 = 9%2A150.

Square both sides. You will get

337%2Ay%5E2+=+%289%2A150%29%5E2+=+1822500%2C+++or+%0D%0A%7B%7B%7By%5E2 = 1822500%2F337 = 5408.012,

Hence, y = sqrt(5408.012}}} = 73.54.

Thus the height of this TV screen is 73.54 in.
Then its wide is x = %2816%2F9%29%2A73.54 = 130.74 in.

Answer. The screen is 130.74 in x 73.54 in.