If a circle is enlarged so that it has a new area that is 25 times the original, what factor were the dimensions changed by?

5

25

625

1/5

If you increase linear dimensions by some factor, then the area

increases by the square of that factor. (I think I told you that in

my answer to a different question earlier today.)

If the area increased by some factor, then the linear dimensions

must have increased by the square root of that factor.

The area is multiplied by 25, so the linear dimensions

must have been multiplied by √25.

I'll leave the last step for you.