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