Question

The least number of square tiles that will be needed to pave a plot 225 m by 30 m is _____

Answer 1

The side of the square tile must be a factor of both 225 and 30, so that no tile needs to be cut.

For least no. of tiles, the size of the tiles should be maximum.
Therefore, from above data we can infer that the side of the tile required should have to be the HCF of the dimensions of the room. Only then will the above condition be satisfied.

So, the side of the square tiles must be the HCF of 225 and 30
225=$3^2\times 5^2$
30 =2 x 3 x 5
So the HCF(225,30) = 3x5 = 15

Therefore the side of the tile is 15m

Area of plot = 225 $\times$ 30
Area of tile = 15 $\times$ 15

No of tiles = area of plot / are of tile
= $\frac{225\times 30}{15\times 15}$
= 30

So 30 tiles of side 15 m are the least number of square tiles required to pave the plot.

Hope this helps.