The floor of a room is 8m 96cm long and 6m 72cm broad. Find the minimum number of square tiles of the same size needed to cover the entire floor.
Answers
To find the minimum number of square tiles to cover the floor, we have to find the greatest size of each such tile. For this purpose, we have to find the H.C.F. of 8m 96cm and 6m 72cm.
8m 96cm = 896 cm and 6m 72cm = 672cm
H.C.F. of 896 and 672
______________
2 | 896, 672
|______________
2 | 448, 336
|______________
2 | 224, 168
|______________
2 | 112, 84
|______________
2 | 56, 42
|______________
7 | 28, 21
|______________
| 4, 3
H.C.F. of 896 and 672 is = 2*2*2*2*2*7 = 224
So, the required size of the square tile must be 224 × 224
Hence, the minimum number of square tiles of same size needed to cover the floor = Area of the floor/Area of one square tile
⇒ (896*672)/(224*224)
⇒ 602112/50176
⇒ 12 square tiles of same size.
Hence, 12 square tiles each of 224cm × 224cm will be needed to cover the entire floor.
Answer.
To find the minimum number of square tiles to cover the floor, we have to find the greatest size of each such tile. For this purpose, we have to find the H.C.F. of 8m 96cm and 6m 72cm.
8m 96cm = 896 cm and 6m 72cm = 672cm
H.C.F. of 896 and 672
______________
2 | 896, 672
|______________
2 | 448, 336
|______________
2 | 224, 168
|______________
2 | 112, 84
|______________
2 | 56, 42
|______________
7 | 28, 21
|______________
| 4, 3
H.C.F. of 896 and 672 is = 2*2*2*2*2*7 = 224
So, the required size of the square tile must be 224 × 224
Hence, the minimum number of square tiles of same size needed to cover the floor = Area of the floor/Area of one square tile
⇒ (896*672)/(224*224)
⇒ 602112/50176
⇒ 12 square tiles of same size.
Hence, 12 square tiles each of 224cm × 224cm will be needed to cover the entire floor.