# 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 largest..possible length of the side of each tile, b)...

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 largest..

possible length of the side of each tile, b) the number of tiles that are needed to cover the floor.

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The length and breadth of the floor = 90m nad 120 meter.

To find the the largest possible measurements of the whole nnumber of tiles he can cover the whole floor.

Since the largest measurement of the tiles is a number that is the greatest factor of both 120 and 90.

Therefore the greatest possible divisor of both 90 120 is the GCD (greatest comon divisor 0 of both 90 and 120.

GCD (120, 90) :

120 = 90*1+30.

30 = 30*3+0.

So GCD (12, 90) = 30.

Therefore the greatest possible measurement of the square tiles is 30m by 30 m .

The number of tiles required to cover the floor = floor area / single tile area = 120*90/30^2 = 12 tiles .

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**