Step by step
The question
Question: find the two equal sides of an isosceles triangle.
The perimeter is 30.
The base is 8.
1 Use the isosceles fact
Isosceles means two sides are equal.
The small marks show which two.
We call each of them x.
2 Write the perimeter
The perimeter is all the sides added: the way round the edge.
So x + x + 8 = 30.
Careful!
30 take away 8 is both equal sides together.
One side is half of it.
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 = 2x.
Now we have 2x + 8 = 30.
We want x by itself.
Two things are stuck to x: times 2 and + 8.
The + 8 is on the outside, so it comes off first.
Then the times 2.
4 Remove the + 8
To remove + 8, we take away 8.
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.
+ 8 and − 8 make zero.
Cross them out.
30 − 8 = 22.
Now we have 2x = 22.
5 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2 divided by 2 is 1.
So just x is left.
22 divided by 2 is 11.
So x = 11!
So each equal side is 11.
6 Check
Let's check: put x = 11 back and add the three sides.
We get the perimeter, 30.
So x = 11 is right!
Let's look back.
First: use the isosceles fact.
Then: write the perimeter.
Then: group like terms.
Then: remove the + 8.
Then: remove the 2.
Last: check.