Step by step
The question
Question: find x.
The two triangles are similar: sides 1.5, 2, 3 and x, 8, 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: 1.5 and x.
The second sides: 2 and 8.
The third sides: 3 and 12.
2 Find the scale factor
The scale factor k says how many times bigger.
We use a pair we know both of: 8 and 2.
k is big over small.
Careful!
The big side goes on top: 8/2, not 2/8.
8 divided by 2 is 4.
Every side of the big triangle is 4 times its partner.
3 Find x
x is in the big triangle.
Its partner in the small one is 1.5.
So x is 1.5 times 4.
That is 6.
So x = 6.
4 Check
Let's check with the other pair: 3 times 4 should be 12.
And x with its partner: 6/1.5 is 4 too.
Every pair has the factor 4.
So x = 6 is right!
Let's look back.
First: match the sides.
Then: find the scale factor.
Then: find x.
Last: check.