Step by step
The question
Question: two similar shapes have areas 16 and 36, and the small side is 10: find the large side.
areas 16 and 36, small side = 10
1 Area factor
The large area divided by the small one: 9/4.
That is k squared.
area factor = 3616 = 94
2 Length scale factor
To go back from k squared to k, we take the square root: 3/2.
k = √(94) = 32
3/2 × 3/2 = 9/4
Careful!
9/4 is the area factor.
Lengths grow less: by its square root.
Careful: not k = 9/4 ✗
3 Use it
10 times 3/2 is 15.
large side = 10 × 32 = 15
4 Check
Let's check: the large side divided by the small one is 3/2, the scale factor.
So it is right!
15 ÷ 10 = 3/2 = k
Let's look back.
First: area factor.
Then: length scale factor.
Then: use it.
Last: check.
Answer
large side = 10 × 32 = 15