James wants to cover a floor measuring 90 cm by 120 cm with square tiles of the same size. Given that he uses only whole tiles, find a) the...

The area of the floor that has to be covered
is:

A = 90*120 cm^2

We'll put
the length of the tile as x.

The number of tiles that
covers the length of the floor:

n =
120/x

The number of tiles that covers the width of the
floor:

m = 90/x

To find the
largest length of the tile, you'll have to determine the highest common factor (or
Greatest Common Divisor) of 90 and 120:

90 =
2*3^2*5

120 = 2^3*3*5

 GCD =
2*3*5 = 30 cm

The largest length of the tiles
is of 30cm.

To find the number of tiles that
are needed to cover the floor, we'll calculate the number of tiles needed to cover the
length of the floor and the number of tiles needed to cover the width of the
floor.

The number of tiles, whose lengths is 30, that
covers the length of the floor is:

n =
120/30

n = 4 tiles

The number
of tiles, whose lengths is 30, that covers the width of the floor
is:

m = 90/30

m = 3
tiles

The total number of tiles needed to
cover the floor:

m*n = 4*3 =
12 tiles