Step by step
The question
Question: find x.
The two triangles are similar: sides 4, 6, 8 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: 4 and 6.
The second sides: 6 and 9.
The third sides: 8 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 4.
k is big over small.
Careful!
The big side goes on top: 6/4, not 4/6.
6 divided by 4 is 1.5.
Every side of the big triangle is 1.5 times its partner.
3 Find x
x is in the big triangle.
Its partner in the small one is 8.
So x is 8 times 1.5.
That is 12.
So x = 12.
4 Check
Let's check with the other pair: 6 times 1.5 should be 9.
And x with its partner: 12/8 is 1.5 too.
Every pair has the factor 1.5.
So x = 12 is right!
Let's look back.
First: match the sides.
Then: find the scale factor.
Then: find x.
Last: check.