Question

A rectangular room is 7m 83 cm long and 5m 13 cm broad. What is the dimension of the largest square tile that can be fixed on the floor completely

Answer 1

Explanation:

The length of the largest tile that can be used is 105.

Step-by-step explanation:

Given : A room is 7m 35 cm broad and 11m 55cm long. The floor of the room is to be covered with square tiles.

To Find  : The length of the largest tile that can be used?

Solution :

Dimension of the room,

Length is 7 m 35 cm

1 m=100 cm

7 m=700 cm

So, Length is 735 cm

Breadth is 11 m 55 cm

1 m=100 cm

11 m=1100 cm

So, Breadth is 1155 cm

Area of the room is

A=L\times BA=L×B

A_r=735\times 1155Ar=735×1155

Size of largest square tile is

H.C.F of 735 and 1155

735=3\times 5\times 7\times 7735=3×5×7×7

1155=3\times 5\times 7\times 111155=3×5×7×11

HCF(735,1155)=3\times 5\times 7HCF(735,1155)=3×5×7

HCF(735,1155)=105HCF(735,1155)=105

Area of 1 tile is

A_t=105\times 105At=105×105

Number of tiles required is

n=\frac{A_r}{A_t}n=AtAr

n=\frac{735\times 1155}{105\times 105}n=105×105735×1155

n=77n=77

The length of the largest tile that can be used is 105.