NR - Wide Screen vs. Full Screen Television Lesson

Math_Lesson_TopBanner.png Wide Screen vs. Full Screen Television

Adapted from Course materials (1.A Student Activity Sheet 4)for AMDM developed under the leadership of the Charles A. Dana Center, in collaboration with the Texas Association of Supervisors of Mathematics and with funding from Greater Texas Foundation.)

                                                                                                                                                                                                                                        Aspect Ratios

Do you prefer to watch movies in full screen or wide screen?

Have you noticed that movies can be offered in two formats? Full screen, the classic television format, usually refers to a width of 4 units or pixels by a height of 3 units, or 4:3. Widescreen video can refer to a number of different aspect ratios, but the most common one has a width of 16 units by a height of 9 units, or 16:9. The newer model television, HDTV, has a 16:9 ratio.

The aspect ratio is the term used to describe the shape of the viewing screen of a picture, video, or movie. It is the ratio of the width to the height of the screen. The width (the bottom) of the display screen is the longer side and the height (the side) is the shorter side of the display screen.

 

When a 16:9 screen displays a 4:3 image, the image is pillar-boxed. The photo of the 4:3 film displayed on the 12:9 screen is an example of pillar-boxing. Notice the vertical gray or black bars that are present on both sides of the screen.  

Letterboxing is a format that creates horizontal gray or black bars at the top and bottom of a 4:3 screen displaying a 16:9 image.  

The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9.

Example: Find the width and height of an older 25-inch television whose screen has an aspect ratio of 4:3.

Twenty-five inches is the measurement of the screen diagonally from corner to corner. One way to do this calculation is using the Pythagorean theorem.

To figure out the lengths of the side of the right triangle, you can use the Pythagorean theorem. a2+b2=c2. C2 equal to 25, but what about a and b? You know that this is a 4:3 aspect television, so substitute those numbers into the theorem as 3x and 4x.

 

 

 

Based on the calculation shown, you know that x equals 5. Therefore in a 4:3 aspect ratio, the length of the television screen is 20 (4 x 5) and the height of the screen is 15 (3 x 5).

What is the area of this screen?  Area is calculated as L x W. So the area of this screen is 20 x 15 = 300. Do not forget your units! 20 inches x 15 inches= 300 square inches. 




You Try:

Find the length and height of a new television set with an aspect ratio of 16:9. The diagonal screen measurement is also 25 inches.

 

 

 

 

 

 

Answer:  

length = 21.76 inches

height = 12.24 inches

Solution:

Solution Equation Length of screen = 16 x 1.36 =21.76 Length of Screen = 9 x 1.36 = 12.24 inches

Answer:

266.34 sq. in

Solution:

length x height = area

21.76 inches x 12.24 inches = 266.34 square inch

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