Step by step
The question
Question: find x.
The two triangles are similar: sides 3, 4, 5 and 9, 12, 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: 3 cm and 9 cm.
The second sides: 4 cm and 12 cm.
The third sides: 5 cm and x.
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 big triangle.
Its partner in the small one is 5.
So x is 5 times 3.
That is 15.
So x = 15 cm.
4 Check
Let's check with the other pair: 4 times 3 should be 12.
And x with its partner: 15/5 is 3 too.
Every pair has the factor 3.
So x = 15 cm is right!
Let's look back.
First: match the sides.
Then: find the scale factor.
Then: find x.
Last: check.