lisa wants to tile her kitchen thats 15 feet x 18 feet. if she is going to use sqaure tiles, what is the greatest possible side length of each tile?
To find the greatest possible side length of the square tiles, we need to determine the dimensions of the largest square that can fit perfectly into the given kitchen area.
The area of Lisa's kitchen is 15 feet x 18 feet = 270 square feet.
Since we are looking for square tiles, the length and width of each tile will be the same.
Let's assume that the side length of each tile is x.
To find the greatest possible side length, we need to look for the largest value of x that can divide the total area of the kitchen exactly.
We can find this by dividing the total area of the kitchen by the area of each tile and finding the largest factor:
270 square feet ÷ x² = 270/x²
Factors of 270: 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 90, 135, 270.
Since we are looking for the largest possible side length, we need to find the highest factor of 270 that is a perfect square.
The highest factor that is a perfect square is 90 (which is equal to 10² × 9).
Therefore, the greatest possible side length of each tile is 10 feet.
To find the greatest possible side length of each tile for Lisa's kitchen, we need to consider the size of the kitchen and find the greatest common factor (GCF) of the dimensions (15 feet and 18 feet).
The GCF of 15 and 18 is 3. This means that the largest square tiles that Lisa can use will have a side length of 3 feet.
Therefore, the greatest possible side length of each tile for Lisa's kitchen is 3 feet.
To find the greatest possible side length of each tile for Lisa's kitchen, we need to consider the dimensions of the kitchen and the size of the tiles.
Since Lisa's kitchen is 15 feet by 18 feet, we want to find the largest square tile that will evenly divide both the length and width of the kitchen.
To find the greatest common divisor (GCD) of 15 and 18, we can list the factors for both numbers:
Factors of 15: 1, 3, 5, 15
Factors of 18: 1, 2, 3, 6, 9, 18
By comparing the factors, we can determine that the GCD of 15 and 18 is 3, which means 3 is the largest square tile that will evenly divide both the length and width of the kitchen.
Therefore, the greatest possible side length of each tile that Lisa can use is 3 feet.