Question

A room 57 m 80 cm long and 47 m 60 cm board is to be paved with equal square tiles. Find the largest title so
that the tiles exactly fit and also find the number of tiles required.​

Answer 1

Answer:

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Answer 2

Answer:

238 square tiles of length 340 cm are required for a room of 5780 x 4760 cm² area.

Step-by-step explanation:

Given,

Length of the room (L) = 57 m + 80cm = 5700 cm + 80 cm = 5780 cm

Width of the room (B) = 47 m + 60 cm = 4700 cm + 60 cm = 4760 cm

To find,

No. of square tiles with side length of 'x'.

Calculation,

As L = 5780 cm = 2 x 2 x 5 x 17 x 17

B = 4760 cm = 2 x 2 x 2 x 5 x 7 x 17

So, for the largest tile we take the G.C.F (L, B)

G.C.F (L, B) = 2 x 2 x 5 x 17

G.C.F(L, B) = 340 cm

Hence, the largest possible side(x) of the square is 340cm.

Now, the area of the square is 340² cm² = 115600 cm²

If 'n' no. of squares fit in a room of 5780 x 4760 cm² area cuboid

then, n x 115600 cm² = 27512800 cm²

n = 238

Therefore, 238 square tiles of length 340 cm are required for a room of 5780 x 4760 cm² area.

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