A room measure 480cm by 560cm find the side of the largest square tile that can used to tile the floor without cutting
480 = 80 * 6
560 = 80 * 7
Looks like a tile with a side of 80cm will do the job
Ar = 480 * 560 = 268,800 cm^2 = Area of room.
sqrt(268,800) = 518.46.
518.46At = 268,800.
At = 518.46 cm^2 = Area of each tile.
L*W = 518.46,
L*L = 518.46,
L^2 = 518.46,
L = 22.77 cm. = Length of a side.
To find the side of the largest square tile that can be used to cover the floor without cutting, we need to find the greatest common divisor (GCD) of the length and width of the room. The GCD represents the largest possible square that can divide both dimensions evenly.
Step 1: Find the GCD of 480 and 560.
We can use the Euclidean algorithm to calculate the GCD. Here's how it works:
- Divide the larger number (560) by the smaller number (480): 560 ÷ 480 = 1 with a remainder of 80.
- Now, divide the previous divisor (480) by the remainder (80): 480 ÷ 80 = 6 with no remainder.
- The remainder is now 0, which means the GCD is the last non-zero remainder, which is 80.
So, the GCD of 480 and 560 is 80.
Step 2: Determine the side of the largest square tile.
The side of the square tile will be equal to the GCD. Therefore, the side of the largest square tile that can be used to tile the floor without cutting is 80 cm.
Note: If the GCD had been 1, it would indicate that there is no common factor between the two dimensions, and hence, a square tile cannot be used without cutting.