Answer:
The homeowner can buy 144 tiles maximum.
Side length = 16 feet.
Step-by-step explanation:
The cost of each tile is $3.45.
So, at $500, the homeowner can buy [tex]\frac{500}{3.45} = 144.92[/tex] ≈ 144 number of tiles. {As the number of tiles can not be a fraction.}
Since each tile is a square with area 256 square inches, so the homeowner can arrange the tiles in 12 by 12 arrangements.
Each tile has side length = √256 = 16 inches.
So, the side length of the largest patio is (16 × 12) inches = 16 feet. (Since, 1 foot = 12 inches). (Answer)