Step by step
The question
Question: find the base of an isosceles triangle.
The two equal sides are 6.
The perimeter is 10.
1 Use the isosceles fact
Isosceles means two sides are equal.
The small marks show which two: both are 6.
We call the base x.
2 Write the perimeter
The perimeter is all the sides added: the way round the edge.
So 6 + 6 + x = 10.
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.
6 + 6 = 12.
Now we have 12 + x = 10.
4 Remove the 12
We want x by itself.
The 12 is in the way.
To remove 12, we take away 12.
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.
12 and − 12 make zero.
Cross them out.
10 − 12 = −2.
So x = −2!
But a side must be longer than 0.
So this is impossible.
Let's look back.
First: use the isosceles fact.
Then: write the perimeter.
Then: group like terms.
Last: remove the 12.