Step by step
The question
Question: find the two equal sides of an isosceles triangle.
The perimeter is 30.
The base is 16.
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 + 16 = 30.
Careful!
30 take away 16 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 + 16 = 30.
We want x by itself.
Two things are stuck to x: times 2 and + 16.
The + 16 is on the outside, so it comes off first.
Then the times 2.
4 Remove the + 16
To remove + 16, we take away 16.
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.
+ 16 and − 16 make zero.
Cross them out.
30 − 16 = 14.
Now we have 2x = 14.
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.
14 divided by 2 is 7.
So x = 7!
But the two equal sides together, 7 + 7 = 14, are not longer than the base, 16.
They cannot meet.
So this is impossible.
Let's look back.
First: use the isosceles fact.
Then: write the perimeter.
Then: group like terms.
Then: remove the + 16.
Last: remove the 2.