# Algebra

I have to explain how I might apply rational expression to my everyday life. I have to explain the application and discuss what the equation might be. Is this a good example?

You go shopping for a big flat-screen HDTV. They always measure TVs diagonally, and HDTV screens have to be in the ratio 16:9, which means that if you divide the width by the height, you would get 16/9, or 1.777777.

You already have an entertainment center and you don't want to buy another one. The space for the TV is 4 feet wide and 3 feet tall.

Neglecting the extra stuff around the edges, how big of a HDTV can you buy to fit your entertainment center?

The width of the space is going to be the determining factor (your entertainment center was designed for "regular" TV sets).

You have 4 feet of width, and since the screen has to be in the ratio of 9:16 (height to width), the maximum height of your screen will be 4 feet × (9/16) = 2.25 feet.

Now, to find the maximum size of the screen, you'll need to use Mr. Pythagoras' famous formula:

a² + b² = c²

4² + 2.25² = c²

16 + 5.0625 = c²

21.0625 = c²

And now...the radical you were looking for:

√21.0625 = c ≈ 4.589 feet

But since all TV screens are measured in inches, you can get as big as a:

4.589 ft × (12 in/ft) = 55 inch screen

Yes, that is a good example. But you'd also better consider the "stuff around the edges"; it might add several inches to the screen size. HDTV does not have a visual display all the way to the edge

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