Liz uses 19 connecting cubes to make a model of house. The house model is in the shape of a rectangle and is one cube high. How many different ways could Liz make the model of the house?
There's only one way to arrange 19 cubes such that a rectangle is formed, and that's by lining them all up in one 19-cube row.
So, 1.
To determine the number of different ways Liz can make the model of the house, we need to find all the possible ways to arrange the 19 connecting cubes into a rectangle shape.
We can approach this problem by considering the different factors of the number 19 and their corresponding pairs.
Since the house model is one cube high, the length of the rectangle can vary. In this case, the length of the rectangle can range from 1 to 19, inclusive.
We can divide the 19 connecting cubes into pairs of numbers that multiply to give 19. Notice that the pairs must consist of one factor less than or equal to the square root of 19 and one factor greater or equal to the square root of 19.
The factors of 19 are (1, 19).
Therefore, the number of ways Liz can make the model of the house is 1.