Glowing Rectangles?
Name_________________________________
Today people spend a lot of time sitting in front of televisions, computers or other electronic devices with
screens. Have you ever noticed that not all screens are the same rectangle? That is to say they are not
proportional or similar. The height to width ratio is not the same when you start comparing analog tube
televisions, HD televisions and movie theatre screens. If you have been to an electronics store recently you
have noticed many similar figures showcased along a wall. I am talking about HD televisions. HD screens
are all similar to teach other. That is the height to width ratio is always the same. The same can be said for
analog tube televisions and for most movie theatre screens and movie formats.
The typical HD screen has a width to height ratio of 16 to 9.
1. Find the missing dimension for each of the HD screens. Assume that all dimensions are in inches.
24
12
6
height = 13.5 inches
width = 21 1/3 inches
width = 10 2/3 inches
48
height = 27
2. Give a length/width dimension that is not similar to this screen type.
Answers will vary tremendously. As long as height/width is not about 1.77, student’s answers will
be correct.
3. An HDTV screen is 40 inches long. What is the height of the screen?
40 16
=
h
9
16h = 360
h = 22.5 inches
4. Sketch your own HD screen below. Make sure to label the side lengths. The screen should be similar to
the other HD screens.
€
5. Here is one type of dimension for a movie theatre screen. Movies and movie theatre screens are
often made in the format 2.35 to 1 (widescreen format, width to height). Find the missing dimensions.
Assume that the dimensions are in feet.
37.6
12
2.35 w
=
1
12
w = 28.2 feet
2.35 37.6
=
1
h
h = 16 feet
6. Is the screen below similar to a movie theatre screen? Show mathematical evidence to support your
€
answer.
€
3
7 2.35
=
3
1
7.05 ≠ 7 ...but close
7
7. I grew up near a giant drive in theatre. The screen was about 150 feet wide. How tall was the screen?
€
2.35 150
=
1
h
h ≈ 63.83
8. Regular, old analog tube television is a 4 to 3 ratio (width to height). Find the missing dimensions.
€Assume all dimensions are in inches.
32
15
4 w
=
3 15
w = 20 inches
4 32
=
3 h
h = 24 inches
9. Give a few different lengths and widths for screens that are similar to the tube screen. You
€might use a ratio table to organize your thinking:
€
length
40
16
24
28
36
44
width
30
12
18
21
27
33
10. For homework measure your own glowing rectangles. Computers, phones, portable video
game systems, digital cameras, I Pod, I Pad, I Phone or anything else with a screen. Find the
dimensions of the screens in millimeters. Use the table below to insert your data:
Product
Length
my LG cell phone
42 mm
Width
30 mm
Simplified Ratio of L:W
1.4: 1
my MacBook
Are any of your screens similar to the widescreen, HD or analog tube screen? Explain.
My LG cell phone is close to the dimensions of an analog screen.
Now it is time to sort the glowing rectangles. Label each as either HD, tube, wide screen or none of
the above.
A
50 mm x 27 mm = 1.85
which is close to HDTV
C
59 mm x 24 mm - close to wide screen
movie dimensions
E
30 mm x 20 mm - close to HDTV
B
40 mm x 30 mm which is analog tube TV
D
82 mm x 27 mm - none of the typical
and doesn’t even look possible
F
78 mm x 35 mm - close to wide screen movie
G
40 mm x 38 mm
none – none of the typical
screens look like squares
H
70 mm x 7 mm
none of the typical dimensions
Funsheet made by Brian Marks, 4/16/2010 Source: http://events.hometheaterforum.com/home/wsfaq.html