Can you make other shaped figures for each of the above three perimeters, or is there only one shape with that perimeter? What is your reasoning?
Perimeter 12 units (smallest): Only one shape — the square.
Perimeter 20 units (largest): Only one shape — the straight line.
Perimeter 18 units: Multiple shapes are possible.
Reasoning: The most compact arrangement (square) and most spread arrangement (line) are unique. Intermediate perimeters can be achieved through multiple configurations.
Explanation
The minimum and maximum perimeters correspond to unique arrangements - the most compact (square) and most spread out (line). However, intermediate perimeters can be achieved through multiple different arrangements of the same 9 squares.
Solution Steps
For perimeter 12 units (smallest), there is only one shape — the square.
For perimeter 20 units (largest), there is only one shape — the straight line.
For perimeter 18 units, multiple shapes are possible.
The most compact arrangement (square) and most spread arrangement (line) are unique.
Intermediate perimeters can be achieved through multiple configurations.