Question

Television sets used to come with an aspect ratio of 4:3 (width is 4 units and height is 3 units). Since broadcast channels in the United States are now broadcasting in 16:9, most newer sets come with a 16:9 aspect ratio. Your brother believes that since you can rewrite the ratio 16:9 as 4^2:3^2, that means a 4:3 television set is similar to a 4^2:3^2 television set. Is this true? What argument would you use to clarify your or your brother’s thinking? What are the dimensions of a television set that would be similar to the 4:3 set?

Answer 1

No, both televisions are not similar.

Aspect ration 12:9 is similar to 4:3

Explanation:

Lets consider it this way.

Aspect ration can be defined as a ratio of width to height.

For a television with aspect ratio 4:3

`3-4=1\\(1)/(3)\cdot100=33\%`

which means that the width will always be 33% greater than the height, which will result in a boxy image.

For a television with aspect ratio 16:9

16 - 9 = 7

`(7)/(9)\cdot100=78\%`

which means that the width will be 78% greater than the height, which will result in a rectangular image.

Hence, both are not the same.

Exact similar dimension to that of 4:3 can be 12:9 because in both, width is 33% greater than height