Question

Emily wants to make a rectangular model with a height of one connecting cube. She wants to make the model in exactly 2 different ways. How many connecting cubes could emily use to make the model in only two ways

Answer 1

Your answer would be 12.

She can use 12 connecting cubes to make the model in only two ways.

Answer 2

6 connecting cubes

Explanation:

Finding rectangular models in two ways is nothing but factorization of a number in two different ways.

Note that 6 is the minimum number with two different factorization 1 x 6 and 2 x 3.

There is another number 4 (< 6) with two different factorization 1 x 4 and 2 x 2 but 2 x 2 will give a square model.

Hence, using 6 connecting cubes, Emily can make one rectangular model with dimensions 1 x 6 and another with dimensions 2 x 3.