Does the order in which I add side lengths affect the perimeter?

Conditions

• The same set of side lengths is being summed.
• Addition is ordinary real-number addition.

Reasoning, step by step

1. List the side lengths of the shape.
2. Add the side lengths in any order.
3. Observe that the final sum remains the same.

Example

Adding $2 + 6 + 2 + 6$ gives 16 ft, and adding $6 + 6 + 2 + 2$ also gives 16 ft.

Common misconceptions

• Believing that the perimeter depends on the sequence in which side lengths are added.

Watch the explanation

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