Step by step
The question
Question: find the base of an isosceles triangle.
The two equal sides are 10.
The perimeter is 32.
1 Use the isosceles fact
Isosceles means two sides are equal.
The small marks show which two: both are 10.
We call the base x.
2 Write the perimeter
The perimeter is all the sides added: the way round the edge.
So 10 + 10 + x = 32.
Careful!
There are two equal sides.
Take both of them away, not one.
3 Group like terms
Terms are the parts between the + and − signs.
Like terms are the same kind: same letters, same powers.
Plain numbers go together.
10 + 10 = 20.
Now we have 20 + x = 32.
4 Remove the 20
We want x by itself.
The 20 is in the way.
To remove 20, we take away 20.
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.
20 and − 20 make zero.
Cross them out.
32 − 20 = 12.
So x = 12!
So the base is 12.
5 Check
Let's check: put x = 12 back and add the three sides.
We get the perimeter, 32.
So x = 12 is right!
Let's look back.
First: use the isosceles fact.
Then: write the perimeter.
Then: group like terms.
Then: remove the 20.
Last: check.