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

Yes, you are correct in considering the "stuff around the edges" of the HDTV, as it might add extra inches to the screen size. In the example given, we neglected this aspect to simplify the calculation. However, in real-life situations, it is essential to take into account the actual visible display area of the HDTV.

To determine the maximum size of the HDTV that can fit your entertainment center, you would need to consider the width constraint. In this case, your entertainment center is 4 feet wide.

Since HDTV screens have a ratio of 16:9, you can determine the maximum height by multiplying the width (4 feet) by the reciprocal of the ratio (9/16). This gives us a maximum height of 4 feet × (9/16) = 2.25 feet.

To find the diagonal size (hypotenuse) of the HDTV screen, you can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let's denote the width as "a," the height as "b," and the diagonal size as "c." According to the Pythagorean theorem, we have:

a² + b² = c²

Plugging in the values from our example:

4² + 2.25² = c²

16 + 5.0625 = c²

21.0625 = c²

To find the diagonal size, we take the square root of both sides:

√21.0625 = √c²

c ≈ 4.589 feet

Since TV screens are generally measured in inches, you can convert the answer to inches by multiplying by 12 inches/foot:

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

So, in this example, the maximum size of the HDTV that can fit your entertainment center is approximately 55 inches.

However, it's important to note that in real-life situations, the actual visible display area may be slightly smaller due to the bezel (the frame surrounding the screen). This is why it's always recommended to consider the visible screen size specified by the manufacturer to ensure it fits properly in your designated space.