The width:height ratio of a television screens is changing from the traditional 4:3 to the widescreen 16:9. If a traditional screen and a widescreen have the same area, then what is the ratio widescreen width:traditional width (Assume that television screens are rectangles).

Let the traditional-format screen have width 1 and height 3/4. Let the new-format screen have width w and height w*9/16.  Then w also represents the ratio of the widths of the two types. The newer screen has area 9 w^2 / 16, and the traditional has area 3/4.

(9/16) w^2 = 3/4
9 w^2 = 12
w^2 = 12/9 = 4/3
w = sqrt(4/3) = 2/sqrt(3) = 2 sqrt(3) / 3 ~= 1.154700538379251

Posted by Charlie on 2007-02-23 09:56:03