Step by step
The question
Question: find x.
The two triangles are similar: sides 8, 10, 12 and 4, x, 6.
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: 8 and 4.
The second sides: 10 and x.
The third sides: 12 and 6.
2 Find the scale factor
The scale factor k says how many times bigger.
We use a pair we know both of: 8 and 4.
k is big over small.
Careful!
The big side goes on top: 8/4, not 4/8.
8 divided by 4 is 2.
Every side of the big triangle is 2 times its partner.
3 Find x
x is in the small triangle.
Its partner in the big one is 10.
The small one is 2 times smaller, so we divide by 2: 10/2.
That is 5.
So x = 5.
4 Check
Let's check with the other pair: 6 times 2 should be 12.
And x with its partner: 10/5 is 2 too.
Every pair has the factor 2.
So x = 5 is right!
Let's look back.
First: match the sides.
Then: find the scale factor.
Then: find x.
Last: check.