meowner is deciding on the size of tiles to use to fully tile a rectangular wall in her bathroom that is 80 inche hches. The tiles are squares and come in three side lengths: 8 inches, 4 inches, and 2 inches. Select all the tr ements about the tiles. A) She will need two 2 -inch tiles to cover the same area as one 4 -inch tile. B) She will need four 4 -inch tiles to cover the same area as one 8 -inch tile. C) Regardless of the size she chooses, she will need the same number of tiles. D) Regardless of the size she chooses, the area of the wall that is being tiled is the same. \( \square \) Ehooses the 8 -inch tiles, she will need \( \frac{1}{16} \) as many tiles as she would with 2 -inch tiles. Fhe cheoses the 8 -inch tiles, she will need a quarter as many tiles as she would with 2 -inch tiles.

To solve this problem, we need to calculate the area of the wall and then determine how many tiles of each size are needed to cover that area. The wall is 80 inches long and we'll assume it's also 80 inches wide for simplicity, as the problem doesn't specify the width. First, let's calculate the area of the wall: Area of the wall = Length × Width Area of the wall = 80 inches × 80 inches Area of the wall = 6400 square inches Now let's look at each statement: A) She will need two 2-inch tiles to cover the same area as one 4-inch tile. - Area of one 2-inch tile = 2 inches × 2 inches = 4 square inches - Area of one 4-inch tile = 4 inches × 4 inches = 16 square inches - Two 2-inch tiles = 2 × 4 square inches = 8 square inches - This statement is false because two 2-inch tiles cover 8 square inches, not the same area as one 4-inch tile. B) She will need four 4-inch tiles to cover the same area as one 8-inch tile. - Area of one 4-inch tile = 4 inches × 4 inches = 16 square inches - Area of one 8-inch tile = 8 inches × 8 inches = 64 square inches - Four 4-inch tiles = 4 × 16 square inches = 64 square inches - This statement is true because four 4-inch tiles cover the same area as one 8-inch tile. C) Regardless of the size she chooses, she will need the same number of tiles. - This statement is false because the number of tiles needed depends on the size of the tiles. D) Regardless of the size she chooses, the area of the wall that is being tiled is the same. - This statement is true because the area of the wall is fixed at 6400 square inches, and the area covered by the tiles will be the same regardless of the tile size. E) If she chooses the 8-inch tiles, she will need \( \frac{1}{16} \) as many tiles as she would with 2-inch tiles. - Area of one 8-inch tile = 64 square inches - Area of one 2-inch tile = 4 square inches - To cover the wall with 8-inch tiles: 6400 square inches / 64 square inches per tile = 100 tiles - To cover the wall with 2-inch tiles: 6400 square inches / 4 square inches per tile = 1600 tiles - Ratio of 2-inch tiles to 8-inch tiles: 1600 tiles / 100 tiles = 16 - This statement is false because she would need 16 times as many 2-inch tiles as 8-inch tiles, not \( \frac{1}{16} \) as many. F) If she chooses the 8-inch tiles, she will need a quarter as many tiles as she would with 2-inch tiles. - This statement is false because, as calculated above, she would need 16 times as many 2-inch tiles as 8-inch tiles, not a quarter as many. So, the correct statements are: B) She will need four 4-inch tiles to cover the same area as one 8-inch tile. D) Regardless of the size she chooses, the area of the wall that is being tiled is the same.