Final answer:
Assuming square tiles that fit perfectly into a square patio, the minimum number of tiles needed to cover 80 square feet would require a 9x9 tile square, which uses 81 tiles. The landscaper has 235 tiles available, so 154 tiles would not be used in this arrangement.
Step-by-step explanation:
The landscaper has 235 tiles to build a square patio with an area of at least 80 square feet. To determine the possible arrangements for the patio, we first need to establish the size of a tile since the area of the patio is determined by the number of tiles and their size. However, since this information is not provided, we will assume that the tiles are square and can be arranged to make a larger square patio. Next, we calculate the minimum number of tiles needed to cover 80 square feet by assuming ideal conditions: square tiles that fit perfectly into a square patio configuration.
We calculate the side length of the square that would have an area of 80 square feet. The side length s of a square with area A is found by the formula s = √A. For an area of 80 square feet:
s = √80 ≈ 8.94 feet.
Since tiles can't be partially used and we're assuming square tiles, we'll need to round up to the next whole number for the number of tiles along each side of the patio, which is 9 tiles per side. If the tiles are 1 foot by 1 foot, then a 9 by 9 square would use 81 tiles, which is more than 80 tiles, so we can arrange the patio as a 9x9 tile square to exceed the minimum area requirement. However, if the tile size varies, the configurations could change as well.
To find out how many tiles are not used in the arrangement, you subtract the number of tiles used in the patio from the total number of tiles available:
235 tiles - 81 tiles used = 154 tiles not used.