Josie wants to tile one square section of her countertop. She bought 850 tiles with side lengths of 1 inch.
A. What is the largest side length of that countertop she can tile? Round to the nearest whole inch.
B. How many tiles will she have left over?
√850 = 29.15
so, she can tile a 29x29 countertop
subtract 29x29 from 850 to get the remainder.
Thanks for the info!
To determine the largest side length of the countertop Josie can tile, we need to find the maximum square that can be created using the 850 tiles. Since each tile has a side length of 1 inch, the total area covered by the tiles will be equal to the area of the countertop.
A. Calculate the area covered by the tiles:
Area of the tiles = number of tiles * area of each tile
Area of the tiles = 850 tiles * (1 inch * 1 inch)
Area of the tiles = 850 square inches
Since the countertop is a square, the largest side length that can be tiled is the square root of the area covered by the tiles.
Square root of 850 square inches ≈ 29.15 inches
Rounded to the nearest whole inch, the largest side length Josie can tile is approximately 29 inches.
B. To determine the number of tiles she will have left over, we need to find the remaining area of the countertop.
Remaining area of the countertop = Area of countertop - Area covered by the tiles
Since the countertop is also a square, the remaining area is equal to:
Remaining area of the countertop = (side length of countertop)^2 - Area covered by the tiles
We determined earlier that the largest side length Josie can tile is approximately 29 inches. Hence,
Remaining area of the countertop = (29 inches)^2 - 850 square inches
Remaining area of the countertop ≈ 841 square inches - 850 square inches
Remaining area of the countertop ≈ -9 square inches
There is a negative value for the remaining area, which implies that Josie cannot tile the entire countertop using the 850 tiles she bought. Therefore, she will have no tiles left over.
To find the largest side length of the countertop that Josie can tile, we need to determine the maximum square that can be formed using 850 tiles.
To do this, we first need to determine the total area covered by the tiles. Since each tile has a side length of 1 inch, the area covered by one tile is 1 inch * 1 inch = 1 square inch.
The total area covered by 850 tiles can be calculated by multiplying the number of tiles by the area covered by one tile. Therefore, the total area covered by the 850 tiles is 850 square inches.
We can determine the side length of the largest square by finding the square root of the total area. Taking the square root of 850 gives us approximately 29.16 inches.
However, we need to round this value to the nearest whole inch, which means rounding up when there is a decimal of 0.5 or greater and rounding down when there is a decimal less than 0.5.
Thus, the largest side length of the countertop Josie can tile is 29 inches.
To find out how many tiles Josie will have left over, we need to subtract the number of tiles used to cover the countertop from the total number of tiles she bought.
In this case, Josie bought 850 tiles, and she used all of them to tile the countertop.
So, she will have 0 tiles left over.