Question

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

I don't know how to do this.

Answer 1

only one way, lay them in a row.

Answer 2

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?

Answer 3

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.

Answer 4

So mixing them up doesn't make it another option?

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

Answer 5

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)

Answer 6

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.