Step by step
The question
Question: find x.
The two triangles are similar: sides 4, 6, 8 and 10, x, 20.
There are four choices.
First we solve it, the normal way.
Then we pick.
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: 4 and 10.
The second sides: 6 and x.
The third sides: 8 and 20.
2 Find the scale factor
The scale factor k says how many times bigger.
We use a pair we know both of: 10 and 4.
How many times bigger?
Big divided by small.
Careful!
The big side goes on top: 10/4, not 4/10.
10 divided by 4 is 2.5.
Every side of the big triangle is 2.5 times its partner.
Because 4 times 2.5 is 10.
3 Find x
x is in the big triangle.
Its partner in the small one is 6.
So x is 6 times 2.5.
That is 15.
So x = 15.
4 Check
Let's check with the other pair: 8 times 2.5 should be 20.
And x with its partner: 15/6 is 2.5 too.
Every pair has the factor 2.5.
So x = 15 is right!
5 Pick the choice
Our answer is x = 15.
That is choice C.
6 Why not the others
A is 2.4.
Wrong: 6 × 4 ÷ 10: the scale factor upside down.
B is 12.
Wrong: 6 + 6: added the same amount; similar shapes grow by multiplying.
D is 60.
Wrong: 6 × 10: forgot to divide by 4.
Let's look back.
First: match the sides.
Then: find the scale factor.
Then: find x.
Then: check.
Then: pick the choice.
Last: why not the others.