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 x = traditional width, y = widescreen width.  The areas of the two screens are as follows:

(3/4)(x^2) = traditional area
(9/16)(y^2) = widescreen area

Set these equal:  (3/4)(x^2) = (9/16)(y^2)

(y^2)/(x^2) = (3/4)/(9/16)

(y^2)/(x^2) = (4/3)

Take square roots:

y/x = [(2√3)/3] ≈ 1.1547 : 1

Posted by hoodat on 2007-02-23 11:09:36