A rectangular veranda is of dimension $18$ m $72$ cm $\times 13$ m $20$ cm. Square tiles of the same dimensions are used to cover it. Find the least number of such tiles.

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4290

4540

4620

4230

answer is A.

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Detailed Solution

Given, the rectangular veranda's edge measures 18 m 72 cm and 13 𝑚 20 𝑐𝑚.
We know that

1 m = 100 cm

.
So, the length is 18m72cm which can be written as,

1800 cm + 72 cm = 1872 cm

Similarly, the breadth is 13m20cm which can be written as,

1300 cm + 20 cm = 1320 cm

We need to find the least number of tiles.
So, finding the HCF of the given dimensions to get the number of tiles,
By using prime factorization finding the HCF of 1872 and 1320, we obtain

1872 = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 13

1320 = 2 \times 2 \times 2 \times 3 \times 5 \times 11

So, the HCF of 1872 and 1320 is

2 \times 2 \times 2 \times 3 = 24

.
Therefore, HCF = 24
Therefore,
No. of tiles required

=

\frac{Area of Veranda}{Area of tiles}

\Rightarrow No . of tiles = \frac{1872 \times 1320}{24 \times 24}

\Rightarrow No . of tiles = 4290

Therefore, the least number of such tiles is 4290.
Hence, option 1 is correct.

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