### A 5.25 m by 3.78 m rectangular courtyard ...

A 5.25 m by 3.78 m rectangular courtyard is to be paved with square tiles of the same size such that only whole tiles are used. What is the largest possible size of such a tile? Also, find the number of tiles required.

Solution

Let a be the edge of the square tile.

Then, $a\times m=5.25$ and $a\times n=3.78$

Dividing, $\frac {m}{n}=\frac {525}{378}$

= $\frac {175}{126}$ [dividing by 3]

= $\frac {25}{18}$ [dividing by 7]

Smallest value of m = 25 and smallest value of n = 18 (for the square tile to be of largest size, m & n should be the least)

Number of tiles = m.n = 25 x 18 = 450

PS: The solution in file format is embedded below.