Question

Find the greatest measure of each stone of same square shape to cover a rectangular courtyard 36metre long and 28metre broad.Find the number of each stones..​

Answer 1

Step-by-step explanation:

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.

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ANSWER

It is given that a rectangular hall is 18m 72cm long and 13m 20cm 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 1872×1320=2471040 and area of the square tile is 24×24=576.

Now, the number of tiles required is:

24×24

1872×1320

=

576

2471040

=4290

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