A gardener has 256 square paving tiles. He wants to arrange the greatest possible number of tiles into a square garden without cutting any tiles. How many tiles will be on each side of the square garden? 21 tiles on each side. 4 tiles on each side. 89 tiles on each side. ‘ 16 tiles on each side.

Answer: 16 tiles on each side.

Step-by-step solution

Step 1: Define the relationship for a square arrangement

Let $s$ denote the number of tiles along one side of the square garden. Because the arrangement forms a solid square grid without cutting tiles, the total number of tiles used is equal to $s^2$ .

Step 2: Calculate the square root of the available tiles

To use the greatest possible number of the 256 tiles, we find the largest whole number whose square is less than or equal to 256. We compute the square root of 256 directly.

Step 3: Evaluate the square root

Since $16 \times 16 = 256$ , 256 is a perfect square. Therefore, exactly 16 tiles can be placed along each side of the square garden.

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