A silly question regarding square meters

Question

Suppose we have two areas: $B$ of size $4m^2$ and $A$ of size $2m^2$. What is the ratio between their sizes?

A simple division would yield 2, but I think that the answer is 4, as illustrated below: A 4x4 square whose area is thus the same as B's.

Could you please clear up the confusion? (E.g. in case the latter option is correct: If a simple division gives the wrong result, how should one approach this problem?)

You are confusing length with area. The squares shown in your diagram each have an area of $2 \times 2=4m^2$, not $2m^2$ — SuperAbound, Aug 01 '14 at 13:48
This is essentially the same mistake as the slaveboy made in Plato's dialogue Meno! — Per Erik Manne, Aug 01 '14 at 14:32

TonyK · Answer 1 · 2014-08-01T14:37:26.063

1

As you pose it, this is really a question about notation: $4m^2$ means four square metres, not 4 metres squared. This is to be expected: in general, $ax^2$ means $a(x)(x)$, not $(ax)(ax)$. So the area of $B$ is twice the area of $A$.

edited Aug 01 '14 at 14:37

answered Aug 01 '14 at 14:25

TonyK

64,559

score 0 · Answer 2 · answered Aug 01 '14 at 14:18

The ratio between their areas is, as you said, 2. (The word "size" is a bit ambiguous, but it's most natural to interpret it as "area" in this context.)

If $A$ and $B$ are both squares, we could also ask the related (but different!) question: what is the ratio between their side lengths? In that case, $A$ would have side length $\sqrt{2} m$ and $B$ would have side length $2 m$, and the ratio of side lengths is $\frac{2}{\sqrt{2}} = \sqrt{2}$.

A silly question regarding square meters

2 Answers2