Associated Topics || Dr. Math Home || Search Dr. Math

### Arranging Blocks in Groups

```
Date: 06/13/98 at 17:31:26
From: Kathy Watson
Subject: Rectangular arrangement of squares

Elise wants to make a rectangular arrangement out of 24 squares. If
one side must be 8 squares, what will be the dimensions of the
rectangle?

I tried to draw a picture but I don't understand this.
```

```
Date: 06/13/98 at 19:47:10
From: Doctor Sorelle
Subject: Re: Rectangular arrangement of squares

Hi Kathy,

Drawing a picture was a very good way to start. Let's do this with a
different problem so that you'll get a chance to work with this one on

What if we want to make a rectangle out of 6 squares? If one side must
be 3 squares, what are the dimensions of the rectangle?

So first let's draw the 6 squares:

[ ]  [ ]  [ ]  [ ]  [ ]  [ ]

Okay, now we just have to rearrange them. But the question gave us
specific instructions for how to rearrange them. First, they have to
be in a rectangle. Second, one of the sides of the rectangle has to be
3 squares long.

Let's put those 3 squares into place together just so we can see what
that would look like:

[ ]  [ ]  [ ]

But now there are still 3 squares left over. How can we include them
in the arrangement? Remember we have to follow the rules. We have
three columns and the remaining 3 squares have to fit into them. I
think they can fit in like this:

[ ]  [ ]  [ ]
[ ]  [ ]  [ ]

So now we have a 3 by 2 rectangle. Do you see why?  We have 3 columns
(up and down, like columns in a building) and 2 rows (left and right,
like rows in a theater).

This problem could also have been done with division and
multiplication. We could have said that we knew we had 6 squares total
and that those 6 squares had to be divided into 3 groups (the
columns).

[ ]    [ ]    [ ]
[ ]    [ ]    [ ]

Then we would have wanted to find the number of squares in each group
(the rows). To do that we would have divided the 6 squares into 3
groups or 6/3 and gotten 2. To get back to the total number of squares
in the rectangle (6) we would have multiplied the dimensions (3 by 2).

Do you think you can do your problem now? If you need more help please
write back.

-Doctor Sorelle,  The Math Forum
Check out our web site! http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Division
Elementary Multiplication

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search