Step by step
The question
Question: find the base of an isosceles triangle.
The two equal sides are 7.
The perimeter is 20.
1 Use the isosceles fact
Isosceles means two sides are equal.
The small marks show which two: both are 7.
We call the base x.
2 Write the perimeter
The perimeter is all the sides added: the way round the edge.
So 7 + 7 + x = 20.
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.
7 + 7 = 14.
Now we have 14 + x = 20.
4 Remove the 14
We want x by itself.
The 14 is in the way.
To remove 14, we take away 14.
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.
14 and − 14 make zero.
Cross them out.
20 − 14 = 6.
So x = 6!
So the base is 6.
5 Check
Let's check: put x = 6 back and add the three sides.
We get the perimeter, 20.
So x = 6 is right!
Let's look back.
First: use the isosceles fact.
Then: write the perimeter.
Then: group like terms.
Then: remove the 14.
Last: check.