Step by step
The question
Question: find the side of an equilateral triangle with perimeter 27.
1 Use the equilateral fact
Equilateral means all three sides are equal.
The marks show it.
We call each side x.
2 Write the perimeter
The perimeter is all three sides added.
So x + x + x = 27.
Careful!
All three sides are the same.
So the perimeter is shared out in 3 equal parts.
3 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
All the x terms go together.
x + x + x = 3x.
Now we have 3x = 27.
4 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
3 divided by 3 is 1.
So just x is left.
27 divided by 3 is 9.
So x = 9!
So each side is 9.
5 Check
Let's check: put x = 9 back and add the three sides.
We get the perimeter, 27.
So x = 9 is right!
Let's look back.
First: use the equilateral fact.
Then: write the perimeter.
Then: group like terms.
Then: remove the 3.
Last: check.