Question

.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.

​

Answer 1

Solution :-

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 2

Given :-

Length of the floor = 8.96 m

Breadth of the floor = 6.72 m

To Find :-

The minimum  number of square tiles of the same size needed to cover the entire floor.

Analysis :-

Find the Highest Common Factor (HCF) of 896 and 672 to get the required size of the tile.

Next using the formulas find the area of the floor and area of one square tile.

Divide area of the floor by area of one square tile in order to get the minimum number of square tiles of same size needed to cover the floor.

Solution :-

We know that,

• l = Length
• b = Breadth
• HCF = Highest Common Factor
• a = Area

Given that,

Length of the floor (l) = 8 m 96 cm = 896 cm

Breadth of the floor (b) = 6 m 72 cm = 672 cm

Finding the HCF of 896 and 672

$\sf HCF=2\times2\times2\times2\times2\times7=224$

Hence, the required size of the square tile is 224 × 224

$\underline{\boxed{\sf Area \ of \ a \ rectangle=Length \times Breadth}}$

Substituting their values, we get

Area of the floor = 896 × 672

Area of the floor = 602112 cm²

Hence, the area of the floor is 602112 cm²

Area of one square tile = 224 × 224

Area of one square tile = 50176 cm²

According to the above info,

The minimum number of square tiles of same size needed to cover the floor would be,

$\longrightarrow \sf \dfrac{Area \ of \ the \ floor}{Area \ of \ one \ square \ tile}$

Substituting their values,

$\sf = \dfrac{602112}{50176}$

$\sf =12$

Therefore, 12 square tiles each will be needed to cover the entire floor.