Posted by **Lee** on Friday, May 6, 2011 at 8:06am.

In how many different ways can you arrange three 4x8 tiles to form a rectangle?

I don't know how to do this.

- Math -
**Reiny**, Friday, May 6, 2011 at 8:08am
only one way, lay them in a row.

- Math -
**Lee**, Friday, May 6, 2011 at 8:21am
But I don't know for example,say you labeled each tile A, B, and C. Is there an option to lay them in different orders, or does that not matter because they are all the same tile? Also is another way, to lay it down as a coloum instead of a row?

- Math -
**Reiny**, Friday, May 6, 2011 at 8:38am
When I said " lay them in a row" I implied in a line.

Row or column would give you the same rectangle

Since you have an odd number, any other way would result in an "L" shape, which is not a rectangle.

- Math -
**Lee**, Friday, May 6, 2011 at 8:40am
So mixing them up doesn't make it another option?

I'm assuming that this problem is a trick question.

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**Reiny**, Friday, May 6, 2011 at 8:45am
I don't know what you mean by "mixing them up". I would assume all 3 tiles would look the same.

You are basically looking for the number of ways that 2 numbers will multiply to get 3.

1x3 is it

e.g. if you had 12 tiles, you could make the following rectangles

1x12

2x6

3x4

So 3 different-shaped rectangles,

(to me a 2x6 rectangle has the same shape as a 6x2 rectangle)

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**Lee**, Friday, May 6, 2011 at 8:49am
Okay I understand. I just wasn't sure if rearranging the tiles (putting them in a different order) would be considered another rectangle. But I get it now. With the answer being 1.

Thank you.

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