SOLUTION: A rectangular courtyard of length 20m 16cm and breadth 15m 60cm is to be paved with same sized square tiles.Find the maximum possible numbers of such tiles?
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Question 843511: A rectangular courtyard of length 20m 16cm and breadth 15m 60cm is to be paved with same sized square tiles.Find the maximum possible numbers of such tiles? Answer by KMST(5328) (Show Source):
You can put this solution on YOUR website! As long as we do not need to be realistic, there is no maximum number of tiles.
In math-land my tiles could measure 1 nanometer by 1 nanometer, and I would use a huge number of those tiles.
There is a minimum number of tiles, corresponding to a maximum tile size, if I am not allowed to cut the tiles into pieces.
To line up a whole number of tiles along the 2016 cm length of the courtyard, I need square tiles with a side length that will go evenly into 2016 cm.
To line up a whole number of tiles along the 1560 cm width of the courtyard, I need square tiles with a side length that will go evenly into 1560 cm.
The tile side length on cm needs to be a factor of 2016 and 1560.
The maximum tile size corresponds to the greatest common factor of 2016 and 1560.
The greatest common factor is
The maximum tile size is by .
We would line up tiles along the length of the courtyard and tiles along the width of the courtyard.
That mean that we would use tiles.
We can also calculate that the surface area of the 24-cm tiles is
while the surface area of the courtyard is
and that it would take times the surface area of one tilew to cover the whole courtyard.
