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 side of each tile,
(b) The number of tiles that are needed to cover the floor.
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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
Maybe this helps you ✨
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