What is the tv screen area in square inches of a

[loukatz]

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

 

[MarkFL]

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

\(\displaystyle \frac{x}{y}=\frac{16}{9}\implies y=\frac{9}{16}x\)

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

\(\displaystyle x^2+y^2=d^2\)

Substituting for $y$, we have:

\(\displaystyle x^2+\frac{81}{256}x^2=d^2\)

\(\displaystyle \frac{337}{256}x^2=d^2\implies x^2=\frac{256}{337}d^2\)

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

\(\displaystyle A=xy=\frac{9}{16}x^2=\frac{144}{337}d^2\)

Now you have a formula to find the area as a function of the diagonal. :)

 

[PeterOwen]

I'm amazed by this forum. How do you know all that?