Question

A movie with an aspect ratio of 2.35:1 is shown as a letterboxed image on an older 25-inch 4:3 television. Find the height of the image, the height of each black bar at the top and bottom of the screen, and the percent of the screen’s area that is occupied by the image. Use a variety of representations to justify your response. Based on your analysis of television aspect ratios, why do you think the consumer market has moved having wide screen TV in the home?

Answer 1

The aspect ratio represents the ratio of the width to the height of a television.  

1. The height of the image on the 25-inch television is 15 inches
2. The height of each black bar is 8.51 inches
3. The percentage of the screen area occupied is 56.73%
4. Consumers moved to screens with wide screen to get clearer images.

The size of a TV is calculated using Pythagoras theorem. Assume the length ratio of the older 25-inch $4:3$ TV is x.

The ratio is represented as:

$Width : Height = 4:3$

 

Using Pythagoras theorem, we have:

$Width^2 + Height^2 = 25^2$

$(4x)^2 + (3x)^2 = 25^2$

$16x^2 + 9x^2 = 625$

$25x^2 = 625$

Divide both sides by 25

$x^2 = 25$

Take positive square roots

$x = 5$

So, the height of the image is:

$Height = 3x$

$Height = 3 \times 5 = 15$

While the width is

$Width = 4x = 4 \times 5 = 20$

Hence, the height of the image is 15 inches

The height of each black bar is calculated as follows:

$Width : Height = 2.35 : 1$

Where

$Width = 20$

So, we have:

$20 : Height = 2.35 : 1$

Express as fraction

$\frac{Height}{20} = \frac{1}{2.35}$

Make Height the subject

$Height = \frac{20}{2.35}$

$Height = 8.51$

The height of each black bar at the top and at the bottom is 8.51 inches

The percentage of the screen’s area that is occupied by the image is calculated using

$\% Screen = \frac{A_1}{A_2} \times 100\%$

Where

$A_1 \to$ Area of black bars

$A_2 \to$ Area of the 25-inch 4:3 television

So, we have:

$A_1 =8.51 \times 20 = 170.2$

$A_2 =15 \times 20 = 300$

$\% Screen = \frac{A_1}{A_2} \times 100\%$ becomes

$\% Screen = \frac{170.2}{300} \times 100\%$

$\% Screen = \frac{170.2}{3} \%$

$\% Screen = 56.73 \%$

Hence, the percentage of the screen area occupied is 56.73%

Consumers moved to TV with a wide screen because a TV with wide screen shows bigger pictures than smaller dimension TV screens,

When the pictures are bigger, the consumers will have a clearer view of what they're watching.

Read more about aspect ratios at:

brainly.com/question/17231027