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How do I solve the following problem? The aspect ratio of a wide-screen TV is 2.39:1....

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catd1115 | Middle School Teacher | (Level 3) Assistant Educator

Posted March 9, 2012 at 9:59 AM via web

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How do I solve the following problem?

  1. The aspect ratio of a wide-screen TV is 2.39:1. Graph the length of the diagonal of a screen as a function of the area of the screen. What is the diagonal of a screen with area 150 in2?

 

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted March 9, 2012 at 10:24 AM (Answer #1)

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The aspect ratio of a wide-screen TV is 2.39 :1.

If one of the sides of the screen is S, the other side is 2.39*S.

The area of the screen is A = 2.39*S^2.

The diagonal of the screen is `sqrt(S^2 + (2.39*S)^2)`

=> `S*sqrt(1 + 2.39^2)`

=> `sqrt(A/2.39)*sqrt(6.7121)`

=> `sqrt A*sqrt(6.7121/2.39)`

The graph of the diagonal as a function of the area is:

When the area of the screen is 150, the diagonal is `(sqrt 150)*sqrt(6.7121/2.39)`

=> 20.5246 in.

The diagonal of a screen with area 150 in^2 is 20.5246 in.

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