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**A mason has to fit a bathroom with square marble tiles of the largest possible size. The size of the bathroom is 10ft. by 8ft. What would be the size in inches of the tile required that has to be cut and how many such tiles are required?**

Answer:

From the question, it’s given that,

Size of bathroom = 10 ft. by 8 ft.

= (10 x 12) inch by (8 x 12) inch [conversion from ft. to inch.]

= 120 inches by 96 inch

Now, the largest size of the tile required will be the HCF of 120 and 96.

So, Applying Euclid’s division lemma

We get,

120 = 96 x 1 + 24

96 = 24 x 4 + 0

⇒ HCF = 24

Thus, we can conclude that the largest size of tile which required is 24 inches And,

Number of tiles required = (area of bathroom) / (area of a tile)

= (120 x 96) / (24x24)

= 5 x 4

= 20 tiles

Therefore, 20 tiles each size 24inch by 24inch are required to be cut.

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