In how many different ways can you arrange three 4 X 8 tiles to form a rectangle?
you can put them end to end, to get a rectangle
24 by 4
you can put them together along their lengths, to get
12 by 8
you can put 2 lengthwise with the third to cap them, to get a 12 by 8
The last two cases result in the same shape of rectangle but the blocks are not arranged the same way.
To calculate the number of different ways to arrange three 4 x 8 tiles to form a rectangle, we can use the concept of permutations.
A permutation is an arrangement of objects in a particular order. In this case, we want to arrange the three tiles to form a rectangle.
To get the number of ways, we need to consider the different orientations the tiles can have while still forming a rectangle.
Let's break down the problem step-by-step:
Step 1: Choose the first tile:
There are three tiles to choose from to be the first tile. So, we have 3 choices for the first tile.
Step 2: Choose the second tile:
After picking the first tile, we have two remaining tiles to choose from for the second tile. So, we have 2 choices for the second tile.
Step 3: Choose the third tile:
Once we have selected the first and second tiles, there is only one tile left to be the third tile.
Multiplying these choices together, we get:
3 choices for the first tile × 2 choices for the second tile × 1 choice for the third tile = 6
Therefore, there are 6 different ways to arrange three 4 x 8 tiles to form a rectangle.