A man wishes to lay square tiles on the floor of a room 12 meters by 18 meters. What is the largest size (in metres) of the square tiles so that a whole number of tiles can be fitted in?
Question
A man wishes to lay square tiles on the floor of a room 12 meters by 18 meters. What is the largest size (in metres) of the square tiles so that a whole number of tiles can be fitted in?
Solution
To determine the largest size of the square tiles that can be used to cover the floor of a room measuring 12 meters by 18 meters, we need to find the greatest common divisor (GCD) of the two dimensions.
Step-by-step solution:
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Identify the dimensions of the room:
- Length: 18 meters
- Width: 12 meters
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Find the GCD of 18 and 12:
- List the factors of 18: 1, 2, 3, 6, 9, 18
- List the factors of 12: 1, 2, 3, 4, 6, 12
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Identify the common factors:
- Common factors of 18 and 12: 1, 2, 3, 6
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Determine the greatest common factor:
- The greatest common factor (GCD) is 6.
Therefore, the largest size of the square tiles that can be used so that a whole number of tiles fit in the room is 6 meters by 6 meters.
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