How do I solve the following problem? The aspect ratio of a widescreen 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...
How do I solve the following problem?

The aspect ratio of a widescreen 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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Expert Answers
justaguide  Certified Educator
The aspect ratio of a widescreen 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.