I've seen a TV comercial that says
Our 60 inch TV have 20% more "visible area" than a 55 inch TV.
I'm curios to know if it's real or not? I need to know formula for relation between rectangle diameter and area then calculate difference between 55 and 60 inch TV.
A wide screen TV have an aspect ratio of 16:9(width:height).
Answer can be more general to say how much visible are we get for any given one inch on a wide screen TV.
This is a super simple question. I hope it is not out of this site context.
Thanks.
1 Answer
Let us suppose that the two TV screens are similar (have the same aspect ratio). If you scale the linear dimensions of an object by the factor $t$, then area is scaled by the factor $t^2$. For example, doubling linear dimensions multiplies area by $4$. In our example, $$t=\frac{60}{55},\qquad\text{and therefore}\qquad t^2=\left(\dfrac{60}{55}\right)^2.$$
It turns out (calculator) that $t^2\approx 1.19008$. So the area has increased by almost exactly $19$ percent. The $20$ percent claim is therefore not much of a stretch.
