Similar shapes, areas 9 and 25, small length 6, find the large length

Step by step

The question

Question: two similar shapes have areas 9 and 25, and the small length is 6: find the large length.

1 Area factor

The large area divided by the small one: 25/9.

That is k squared.

2 Length scale factor

To go back from k squared to k, we take the square root: 5/3.

Careful!

25/9 is the area factor.

Lengths grow less: by its square root.

3 Use it

6 times 5/3 is 10.

4 Check

Let's check: the large length divided by the small one is 5/3, the scale factor.

So it is right!

Let's look back.

First: area factor.

Then: length scale factor.

Then: use it.

Last: check.