Step by step
The question
Question: A rectangle is twice as long as it is wide.
Its perimeter is 42 m.
Find the length and the width.
1 Find what we know
What do we know?
The length is 2 times the width.
The perimeter is 42 m.
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 2 times the width: 2x.
Let's draw it.
The long sides are 2x.
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 + 2x + x + 2x = 42.
Now we solve it.
4 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 + 2x + x + 2x = 6x.
Now we have 6x = 42.
5 Remove the 6
6x means 6 times x.
We want just x.
To remove times 6, we divide by 6.
We do it on both sides, so they stay equal.
6 divided by 6 is 1.
So just x is left.
42 divided by 6 is 7.
So x = 7!
6 Answer the question
The length is 2x: 2 × 7 = 14.
So the width is 7 m and the length is 14 m.
7 Check
Let's check in the story.
All the way round: 7 + 14 + 7 + 14 = 42, like the story says.
And the length is 2 times the width.
Does it make sense?
The length, 14 m, is longer than the width, 7 m.
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.