Question

Find the Minimum Number of Tiles
Rectangular courtyard 3.78 m long and 5.25 m wide is to be paved exactly with square tiles all of the same sizes. Find the minimum number of tiles?

Answer 1

To find the answer for this we will calculate the greatest common divisor of the two figures(the length and width of the courtyard).

3.78m= 378 cm
5.25m= 525 cm

factors for 378= 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
                           (378 is divisible by all these numbers)

factors for 525= 1,3,5,7,15,21,25,35,75,105,175,525
                              (525 is divisible by all these numbers)

Therefore the greatest common divisor of the two numbers, from their factors, is 21.
We use the greatest divisor so that we can have the least number of tiles.


Therefore to get number of tiles :
the length of the square tiles will be 21 cm by 21 cm


area of the court = 378 x 525 / (21 x 21)
                           = 198450/441
                           = 450
                         
Therefore the minimum number of tiles = 450 tiles