Similar shapes, areas 25 and 64, large width 16, find the small width

Step by step

The question

Question: two similar shapes have areas 25 and 64, and the large width is 16: find the small width.

1 Area factor

The large area divided by the small one: 64/25.

That is k squared.

2 Length scale factor

To go back from k squared to k, we take the square root: 8/5.

Careful!

64/25 is the area factor.

Lengths grow less: by its square root.

3 Use it

16 divided by 8/5 is 10.

4 Check

Let's check: the large width divided by the small one is 8/5, the scale factor.

So it is right!

Let's look back.

First: area factor.

Then: length scale factor.

Then: use it.

Last: check.