Similar shapes, areas 4 and 49, large length 14, find the small length

Step by step

The question

Question: two similar shapes have areas 4 and 49, and the large length is 14: find the small length.

1 Area factor

The large area divided by the small one: 49/4.

That is k squared.

2 Length scale factor

To go back from k squared to k, we take the square root: 7/2.

Careful!

49/4 is the area factor.

Lengths grow less: by its square root.

3 Use it

14 divided by 7/2 is 4.

4 Check

Let's check: the large length divided by the small one is 7/2, the scale factor.

So it is right!

Let's look back.

First: area factor.

Then: length scale factor.

Then: use it.

Last: check.