Step by step
The question
Question: find x.
The two triangles are similar: sides x, 6, 8 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: 6 and 9.
The third sides: 8 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 6.
k is big over small.
Careful!
The big side goes on top: 9/6, not 6/9.
9 divided by 6 is 1.5.
Every side of the big triangle is 1.5 times its partner.
3 Find x
x is in the small triangle, so we go from big to small.
1.5 is 3/2.
Turned upside down, it is 2/3.
So x is 6 times 2/3.
Times 2: 6 times 2 is 12.
Over 3: 12 divided by 3 is 4.
That is 4.
So x = 4.
4 Check
Let's check with the other pair: 8 times 1.5 should be 12.
And x with its partner: 6/4 is 1.5 too.
Every pair has the factor 1.5.
So x = 4 is right!
Let's look back.
First: match the sides.
Then: find the scale factor.
Then: find x.
Last: check.