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Question

A rectangular hall is 18m 72cm long and 13m 20cm broad. It is to be paved with square tiles of the same size. Find the least possible number of such tiles.


Solution

It is given that a rectangular hall is $$18$$m $$72$$cm long and $$13$$m $$20$$cm broad which means that rectangular hall is $$1872$$ cm long and $$1320$$ cm broad.

The given integers $$1872$$ and $$1320$$ can be factorised as follows:

$$1872=2×2×2×2×3×3×13\\ 1320=2×2×2×3×5×11$$

We know that $$HCF$$ is the highest common factor, therefore, the $$HCF$$ of $$1872$$ and $$1320$$ is:

$$HCF=2×2×2×3=24$$

Therefore, maximum side of the square is $$24$$ cm and 

Since, area of rectangular courtyard is $$1872\times 1320=2471040$$ and area of the square tile is $$24\times 24=576$$.

Now, the number of tiles required is:

$$\dfrac { 1872×1320 }{ 24×24 } =\dfrac { 2471040 }{ 576 } =4290$$

Hence, the least possible number of such tiles is $$4290$$.

Maths

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