Step by step
The question
Question: find x.
The two triangles are similar: sides 5, 12, 13 and 15, 36, x.
1 Match the sides
Similar means the same shape, with the same angles.
One triangle is a bigger copy of the other.
A bigger copy keeps the order of the sides.
So the shortest goes with the shortest, the longest with the longest.
The question gives the sides in matching order: first with first.
The first sides go together: 5 and 15.
The second sides: 12 and 36.
The third sides: 13 and x.
2 Find the scale factor
The scale factor k says how many times bigger.
We use a pair we know both of: 15 and 5.
How many times bigger?
Big divided by small.
Careful!
The big side goes on top: 15/5, not 5/15.
15 divided by 5 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 13.
So x is 13 times 3.
That is 39.
So x = 39.
4 Check
Let's check with the other pair: 12 times 3 should be 36.
And x with its partner: 39/13 is 3 too.
Every pair has the factor 3.
So x = 39 is right!
5 Type it in
The answer box takes 5 characters.
39 has 2.
It fits.
We type 39.
Let's look back.
First: match the sides.
Then: find the scale factor.
Then: find x.
Then: check.
Last: type it in.