MHB What is the tv screen area in square inches of a

AI Thread Summary
The discussion focuses on calculating the screen area of various TV sizes with a 16:9 aspect ratio, using the diagonal measurement. The formula derived for the area (A) in square inches is A = (144/337) * d², where d is the diagonal length. This allows for quick calculations of screen area for 40, 60, 65, 80, and 86-inch TVs. The calculations utilize the Pythagorean theorem and the aspect ratio to establish the relationship between width and height. The derived formula provides a straightforward method to determine the screen area based on diagonal size.
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Assume that the ratio of a big screen TV is 16:9. TVs are advertised by their diagonal (sp?) length. What is the screen area in square inches of a:

a) 40 inch TV

b) 60 inch TV

c) 65 inch TV

d) 80 inch TV

e) 86 inch TV

Show the formula (equation) that you used.

Thank you
 
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Let's let $x$ be the width of the screen and $y$ be the height, and so we have:

$$\frac{x}{y}=\frac{16}{9}\implies y=\frac{9}{16}x$$

Let $d$ be the diagonal measure of the screen...by Pythagoras we have:

$$x^2+y^2=d^2$$

Substituting for $y$, we have:

$$x^2+\frac{81}{256}x^2=d^2$$

$$\frac{337}{256}x^2=d^2\implies x^2=\frac{256}{337}d^2$$

Now, the area $A$ of the screen is:

$$A=xy=\frac{9}{16}x^2=\frac{144}{337}d^2$$

Now you have a formula to find the area as a function of the diagonal. :)
 
I'm amazed by this forum. How do you know all that?
 
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