Ender W.

# If I have a square "A" with side length 5 and a square "B" with side length 10. What is the scale factor from A to B? Is it 1/2 or 2?

If I have a square "A" with side length 5 and a square "B" with side length 10. What is the scale factor from A to B? Is it 1/2 or 2.

I have seen it both ways in textbooks and the internet. If they just similar shapes then it is 1/2 but if it is a dilation then it is 2, is that correct?

## 2 Answers By Expert Tutors

By:

Tutor
4.9 (100)

Ender W.

Thank you for answering. I understand that this represents an enlargement and therefore the scale factor should be 2, but more than one place has given the definition as: The scale factor of A to B is the ratio of side length A to the side length of B, which would be the reciprocal.
Report

12/04/14 David W.

tutor
I can see your confusion.  The RATIO is 1:2, also written as 1/2.  If we have 5 red books and 10 black books, then the ratio of red to black is 5/10 or 1/2, but the SCALE FACTOR is still 2, since that is what we are multiplying by.

If you need to think of it as taking the reciprocal, then yes, that is what you do. A ratio of 1/3 would give us a scale factor of 3, and a ratio of 3/1 would give us a scale factor of 1/3.
Report

12/04/14 David W.

tutor
As I read more, I see that some places list the scale factor as the ratio of larger/smaller, so our ratio in that case would be 2/1, making our scale factor 2.

The best way to think about it is that the scale factor is what you have to multiply one by to get the other, as explained earlier. This can be figured out by taking the reciprocal of the ratio.  If we had 2/3, we have to multiply 2 x 3/2 = 3, so our scale factor is 3/2.

Confusing? Yes, but hopefully less so.
Report

12/04/14 Tutor
5.0 (323)

Math and Test Prep Teacher - M.Ed

Ender W.

Thank you for answering. How is 1:2 or 1/2 giving us a scale factor of 2? Do we always take the reciprocal of the reduced fraction?
Report

12/04/14

## Still looking for help? Get the right answer, fast.

Get a free answer to a quick problem.
Most questions answered within 4 hours.

#### OR

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.