Worked examples
The question
Question: find x.
The two triangles are similar: sides 3, 4, 5 and 6, 8, 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 and 6.
The second sides: 4 and 8.
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: 6 and 3.
k is big over small.
k = 63
Careful!
The big side goes on top: 6/3, not 3/6.
Careful: big over small
6 divided by 3 is 2.
Every side of the big triangle is 2 times its partner.
k = 2
3 Find x
x is in the big triangle.
Its partner in the small one is 5.
So x is 5 times 2.
x = 5 × 2
That is 10.
So x = 10.
x = 10
4 Check
Let's check with the other pair: 4 times 2 should be 8.
4 × 2 = 8
And x with its partner: 10/5 is 2 too.
105 = 2
Every pair has the factor 2.
So x = 10 is right!
Let's look back.
First: match the sides.
Then: find the scale factor.
Then: find x.
Last: check.
▶ Watch it solved
The question
Question: find x.
The two triangles are similar: sides 6, x, 10 and 3, 4, 5.
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: 6 and 3.
The second sides: x and 4.
The third sides: 10 and 5.
2 Find the scale factor
The scale factor k says how many times bigger.
We use a pair we know both of: 6 and 3.
k is big over small.
k = 63
Careful!
The big side goes on top: 6/3, not 3/6.
Careful: big over small
6 divided by 3 is 2.
Every side of the big triangle is 2 times its partner.
k = 2
3 Find x
x is in the big triangle.
Its partner in the small one is 4.
So x is 4 times 2.
x = 4 × 2
That is 8.
So x = 8.
x = 8
4 Check
Let's check with the other pair: 5 times 2 should be 10.
5 × 2 = 10
And x with its partner: 8/4 is 2 too.
84 = 2
Every pair has the factor 2.
So x = 8 is right!
Let's look back.
First: match the sides.
Then: find the scale factor.
Then: find x.
Last: check.
▶ Watch it solved
The question
Question: find x.
The two triangles are similar: sides 2.5, 3, 4 and 5, 6, 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: 2.5 and 5.
The second sides: 3 and 6.
The third sides: 4 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 2.5.
k is big over small.
k = 52.5
Careful!
The big side goes on top: 5/2.5, not 2.5/5.
Careful: big over small
5 divided by 2.5 is 2.
Every side of the big triangle is 2 times its partner.
k = 2
3 Find x
x is in the big triangle.
Its partner in the small one is 4.
So x is 4 times 2.
x = 4 × 2
That is 8.
So x = 8.
x = 8
4 Check
Let's check with the other pair: 3 times 2 should be 6.
3 × 2 = 6
And x with its partner: 8/4 is 2 too.
84 = 2
Every pair has the factor 2.
So x = 8 is right!
Let's look back.
First: match the sides.
Then: find the scale factor.
Then: find x.
Last: check.
▶ Watch it solved
