Step by step
The question
Question: find x.
The two triangles are similar: sides 3, 4, 5 and 6, 9, x.
1 Match the sides
Similar means the same shape.
One triangle is a bigger copy of the other.
Matching sides go together: the shortest with the shortest, the longest with the longest.
Here both lists go in the same order.
The first sides go together: 3 and 6.
The second sides: 4 and 9.
The third sides: 5 and x.
2 Find the scale factor
The scale factor k says how many times bigger.
We use a pair we know both of: 6 and 3.
k is big over small.
Careful!
The big side goes on top: 6/3, not 3/6.
6 divided by 3 is 2.
Every side of the big triangle is 2 times its partner.
But the other pair gives 9 divided by 4, that is 2.25.
Not the same factor.
So these triangles are not similar.
There is no answer.
Let's look back.
First: match the sides.
Last: find the scale factor.