# Algebra

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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?

Answer:

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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