Television transition
Weekly Problem 15 - 2006
What is the relationship between the width of wide screen and traditional televisions if the area of the two screens is the same?
What is the relationship between the width of wide screen and traditional televisions if the area of the two screens is the same?
Age
11 to 16
Challenge level
Problem
The ratio width : height of 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 ?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Let the widescreen width and traditional width be $w$ and $W$ respectively. Then the respective heights are $\frac{9w}{16}$ and $\frac{3W}{4}. $ As the areas are equal: $$x \times \frac{9w}{16} = W \times \frac{2W}{4}$$ i.e. $$w^2 = \frac {4}{3}W^2$$ Hence $w : W = 2 : \sqrt{3}$.