Use 17 connecting cubes to make a kitchen model. Model is is the shape of rectangle and is one cube high. How many different ways to make the model?
To solve this problem, let's break it down step-by-step:
Step 1: Determine the dimensions of the kitchen model.
Since the model is in the shape of a rectangle, let's assume the length of the rectangle is L and the width is W.
Step 2: Determine the number of connecting cubes needed to create the model.
Since the model is one cube high and made up of connecting cubes, the total number of cubes needed for the model would be the same as the area of the rectangle.
Step 3: Calculate the possible dimensions of the rectangle.
Since we have 17 connecting cubes available, the possible dimensions of the rectangle can range from (1, 17) to (17, 1), including both square and non-square rectangles.
Step 4: Calculate the number of different ways to make the model.
To calculate the number of ways, we need to find all possible combinations of L and W such that L * W is equal to 17. Counting these combinations will give us the number of different ways to make the kitchen model.
Assuming that the length L and width W both need to be integers, we can list out all the possible combinations:
(1, 17)
(17, 1)
(2, 8)
(8, 2)
(4, 4)
Hence, there are 5 different ways to make the kitchen model using 17 connecting cubes.
To find the different ways to make a kitchen model using 17 connecting cubes, we need to consider the dimensions of the rectangle.
Since the model is one cube high, we can assume that the 17 connecting cubes will form the length and width of the rectangle.
Let's consider the possible dimensions of the rectangle:
1. If the rectangle is 1 cube wide, then it will have a length of 17 cubes. In this case, the model can be arranged in one way.
2. If the rectangle is 2 cubes wide, then it will have a length of 8 cubes. We can arrange the model by placing the two cubes either vertically or horizontally. Thus, there are two ways to arrange the model.
3. If the rectangle is 3 cubes wide, then the length will be 5 cubes. Again, we can arrange the model by placing the three cubes either vertically or horizontally. So, there are two ways to arrange the model.
4. If the rectangle is 4 cubes wide, then the length will be 4 cubes. Here, we can only arrange the model by placing the four cubes vertically. Hence, there is only one way to arrange the model.
Since a rectangle cannot have a width larger than its length, we can stop here as no other arrangements are possible.
In total, there are 1 + 2 + 2 + 1 = 6 different ways to make the kitchen model using 17 connecting cubes.