Aroom measures 540 cm by 420 . Find the length of the largest square tiles that can be used to cover the floor without requiring any cutting .
GCF(540,420) = 60
So, if 60-cm tiles are used, the floor is 9x7 tiles
respect
A room measures 540m by 4200m Find the area of the largest Square tile that can be used to Cover the floor without and cutting??
Well, let's do some math! To find the length of the largest square tiles that can be used to cover the floor without requiring any cutting, we need to find the greatest common divisor (GCD) of the dimensions of the room.
The GCD of 540 cm and 420 cm is... drumroll, please... 60 cm! So, the length of the largest square tiles that can be used to cover the floor without cutting is 60 cm.
But hey, don't worry, I'll make sure those tiles don't have any y traps. Safety first, always!
To find the length of the largest square tiles that can be used to cover the floor without requiring any cutting, we need to find the greatest common divisor (GCD) of the dimensions of the room.
The dimensions of the room are given as 540 cm by 420 cm. To find the GCD, we can use the Euclidean algorithm.
Step 1: Find the remainder when the larger number is divided by the smaller number.
- 540 ÷ 420 = 120, with a remainder of 120.
Step 2: Replace the larger number with the smaller number and the smaller number with the remainder.
- Now, we have 420 ÷ 120 = 3, with a remainder of 60.
Step 3: Repeat the process of finding the remainder until we have a remainder of 0.
- Continuing, we have 120 ÷ 60 = 2, with no remainder.
- Finally, 60 ÷ 0 = Undefined.
Since we have reached a remainder of 0, the process stops. The GCD of 540 and 420 is the last nonzero remainder, which is 60.
Therefore, the length of the largest square tiles that can be used to cover the floor without requiring any cutting is 60 cm.