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Explications étape par étape:
To cover a square toilet entirely with rectangular tiles of sides 60cm by 48cm, we need to find the least possible area of the room that accommodates these tiles.
First, let's calculate the area of one tile: Area of one tile = length × width = 60 cm × 48 cm = 2880 square centimeters = 0.288 square meters (since 1 square meter = 10,000 square centimeters)
To find the least possible area of the room, we need to consider how these tiles fit into the square space. The least area would be achieved when the tiles cover the maximum possible area without leaving gaps.
Now, let's find the greatest common divisor (GCD) of 60 and 48:
GCD(60, 48) = 12
This means the greatest common side that perfectly fits both 60 and 48 is 12cm.
To cover the square toilet, the length and width of the sides should be a multiple of this GCD. Thus, the least possible side length of the square toilet that these tiles could cover without leaving any gap would be 60cm + 12cm = 72cm.
So, the least possible area of the room accommodating these tiles would be the area of the square with a side length of 72cm.
Area of the square = side × side = 72 cm × 72 cm = 5184 square centimeters = 0.5184 square meters
Therefore, the least possible area of the room (in square meters) that could accommodate these tiles covering the square toilet is 0.5184 square meters.