# Mathematics Exercise

Most pool specialists suggest installing a border of at least two rows of square tiles around the entire pool. Your neighbor, who has a square pool measuring 8 feet on each side, has decided to follow that suggestion, using medium square tiles that measure 1 foot by 1 foot. A diagram of the pool is shown below.

1.You’d like to find an easy way to calculate the number of tiles (N) needed to tile around a square pool with a side length of “s”, assuming you use the recommended two rows.

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2. Find a formula in terms of “s” that can be used to calculate the total number of tiles needed (N). Do not simplify your formula in any way.

3. Then, use a completely different method to write a formula for “N” in terms of “s”. Once again, do not simplify it, and show that the formulas are equivalent using one or more of the properties that you have studied (commutative, associative, distributive). Indicate when any of these properties is being used in your work.