Step by step
The question
Question: A rectangle is 3 cm longer than it is wide.
Its perimeter is 26 cm.
Find the length and the width.
1 Find what we know
What do we know?
The length is 3 cm more than the width.
The perimeter is 26 cm.
Perimeter means all the way round.
What do we want?
The length and the width.
2 Name the unknown
We know the length from the width.
So we call the width x.
The length is 3 more: x + 3.
Let's draw it.
The long sides are x + 3.
The short sides are x.
3 Write the equation
All the way round: we add the four sides.
Width, length, width, length.
So the equation is x + (x + 3) + x + (x + 3) = 26.
Now we solve it.
4 Open the brackets
A bracket with a plus or nothing in front can just be removed.
5 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.
Plain numbers go together.
x + x + x + x = 4x.
3 + 3 = 6.
Now we have 4x + 6 = 26.
We want x by itself.
Two things are stuck to x: times 4 and + 6.
The + 6 is on the outside, so it comes off first.
Then the times 4.
6 Remove the + 6
To remove + 6, we take away 6.
We do it on both sides, so they stay equal.
+ 6 and − 6 make zero.
Cross them out.
26 − 6 = 20.
Now we have 4x = 20.
7 Remove the 4
4x means 4 times x.
We want just x.
To remove times 4, we divide by 4.
We do it on both sides, so they stay equal.
4 divided by 4 is 1.
So just x is left.
20 divided by 4 is 5.
So x = 5!
8 Answer the question
The length is x + 3: 5 + 3 = 8.
So the width is 5 cm and the length is 8 cm.
9 Check
Let's check in the story.
All the way round: 5 + 8 + 5 + 8 = 26, like the story says.
And the length is 3 more than the width.
Does it make sense?
The length, 8 cm, is longer than the width, 5 cm.
So the answer is right!
Let's look back.
First: find what we know.
Then: name the unknown.
Then: write the equation.
Then: solve it.
Then: answer the question.
Last: check.