Step by step
The question
Question: find x.
The two triangles are similar: sides 2, 4, 5 and 5, 10, 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: 2 and 5.
The second sides: 4 and 10.
The third sides: 5 and x.
2 Find the scale factor
The scale factor k says how many times bigger.
We use a pair we know both of: 5 and 2.
k is big over small.
Careful!
The big side goes on top: 5/2, not 2/5.
5 divided by 2 is 2.5.
Every side of the big triangle is 2.5 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 2.5.
That is 12.5.
So x = 12.5.
4 Check
Let's check with the other pair: 4 times 2.5 should be 10.
And x with its partner: 12.5/5 is 2.5 too.
Every pair has the factor 2.5.
So x = 12.5 is right!
Let's look back.
First: match the sides.
Then: find the scale factor.
Then: find x.
Last: check.