Step by step
The question
Question: find x.
The two triangles are similar: sides 2, 3, 4 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: 2 and 6.
The second sides: 3 and 9.
The third sides: 4 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 2.
k is big over small.
Careful!
The big side goes on top: 6/2, not 2/6.
6 divided by 2 is 3.
Every side of the big triangle is 3 times its partner.
3 Find x
x is in the big triangle.
Its partner in the small one is 4.
So x is 4 times 3.
That is 12.
So x = 12.
4 Check
Let's check with the other pair: 3 times 3 should be 9.
And x with its partner: 12/4 is 3 too.
Every pair has the factor 3.
So x = 12 is right!
Let's look back.
First: match the sides.
Then: find the scale factor.
Then: find x.
Last: check.