Question

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Answer 1

Answer:

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 stone is 24×24=576.

Now, the number of stones required is:

24×24

1872×1320

=

576

2471040

=4290

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

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

The dimensions of courtyard are

Length = 21m 36cm = 2136cm

Breadth = 17m 4cm = 1704cm

Least possible side of square stones used = HCF of 2136 and 1704

We know that the prime factorization of 2136 = 2 x 2 x  2 x 3 x 89

1704 = 2 x 2 x 2 x 3 x 71

So HCF of 2136 and 1704 = 2 × 2 × 2 × 3 = 24

Hence, the least possible side of square stones used is 24cm.

We know that

No. of square stones which is used to pave the rectangular courtyard = Area of courtyard/ Area of stone By substituting the values

No. of square stones which is used to pave the rectangular courtyard = (2136 × 1704)/ (24)2 = 75,828 Therefore, the least possible number of such stones is 75,828.