Questions: The following composite solid has all congruent edges. Which of the following is not a possible way to divide the figure? two congruent rectangular prisms two congruent rectangular prisms and one cube two congruent cubes and one rectangular prism five congruent cubes

The following composite solid has all congruent edges. Which of the following is not a possible way to divide the figure?
two congruent rectangular prisms
two congruent rectangular prisms and one cube
two congruent cubes and one rectangular prism
five congruent cubes

Transcript text: The following composite solid has all congruent edges. Which of the following is not a possible way to divide the figure? two congruent rectangular prisms two congruent rectangular prisms and one cube two congruent cubes and one rectangular prism five congruent cubes

Solution

Solution Steps

Step 1: Analyze the given solid

The given solid is composed of five congruent cubes.

Step 2: Consider the first option

Two congruent rectangular prisms: We can divide the figure into two congruent rectangular prisms. One prism can consist of the three cubes on the left, and the other can consist of the two cubes on the right. These two prisms would be mirror images of each other and congruent.

Step 3: Consider the second option

Two congruent rectangular prisms and one cube: We can take the central cube and consider it as a separate cube. The remaining four cubes can be divided into two congruent rectangular prisms.

Step 4: Consider the third option

Two congruent cubes and one rectangular prism: This is not possible. If we take two cubes separately, the remaining three cubes cannot form a rectangular prism. If we try to form two cubes by joining two individual cubes together, it wouldn't be possible to keep the remaining part as a single rectangular prism.

Step 5: Consider the fourth option

Five congruent cubes: The figure is given to be made of five congruent cubes.