Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.


share|cite|improve this question
up vote 4 down vote accepted

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.

share|cite|improve this answer
Thanks. Is it same for 16:9 aspect ratio? – Mohsen Nov 22 '11 at 0:33
Yes, this works for all postive ratios. – The Chaz 2.0 Nov 22 '11 at 0:36
Can you say we get 19/5 percent for any one more inch on TV? I mean is this relation work for like 32 inch to 37 inch too? I updated my question – Mohsen Nov 22 '11 at 0:39
For $32$ to $37$, the ratio of areas is $(37/32)^2$, which is about $1.337$. So you gain almost $34$ percent in area. If you go from $100$ inch to $105$ inch, the gain in area is only about $10$ percent. Adding $5$ inches to a smallish TV has a more dramatic relative effect than adding $5$ inches to a big TV. – André Nicolas Nov 22 '11 at 0:46

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.