Question

Floors of a room is to be fitted with square marbles tiles of largest possible size. The size of room is 10m x 7m. What should be the size of the tiles that has to be cut and how many such tiles are required?

Answer 1

Solution :-

Least number of square tiles are required if the side of the square tile is the H.C.F. of the length and breadth.

length of the room = 10 m
Breadth of the room = 7 m

H.C.F. of 10 and 7

10 = (7*1) + 3
7 = (3*2) + 1
3 = (1*3) + 0 

So, H.C.F. of 10 and 7 is 1

Therefore, the length of the square tile is 1 m

Area of 1 square tile = 1*1 = 1 sq m

Area of the room = 10*7 = 70 sq m

Number of square tile required each measuring 1m × 1m = 70/1
= 70 tiles
 
Hence, the size of each square tile is 1m × 1m and 70 square tiles will be required. 

Answer.

Answer 2

SOLUTION:

Least number of square tiles are required if the side of the square tile is the H.C.F. of the length and breadth.

length of the room = 10 m

Breadth of the room = 7 m

H.C.F. of 10 and 7

10 = (7*1) + 3

7 = (3*2) + 1

3 = (1*3) + 0 

So, H.C.F. of 10 and 7 is 1

Therefore, the length of the square tile is 1 m

Area of 1 square tile = 1*1 = 1 sq m

Area of the room = 10*7 = 70 sq m

Number of square tile required each measuring 1m × 1m = 70/1

= 70 tiles

Hence, the size of each square tile is 1m × 1m and 70 square tiles will be required.

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