Question

The length and breadth of a room are 13m and 7.5m, respectively. the floor of the room is to be paved with square tiles of uniform size. determine the length of the largest possible size of the tile?

Answer 1

Area of the room = (1300*750)cm^2
                            = 975000cm^2

To find the length of the largest possible tile we need to factorize 975000

Factorizing 975000, we get --  5^4 * 2^2 * 13 * 3

Since 5^4 * 2^2 is a perfect square (square of 5^2 * 2), it's root will be the size of tiles and 13 * 3 will be the number of tiles.

Therefore the length of the tiles = 5^2 * 2  
                                                   = 50cm                            

Answer 2

Answer:

Length = 9.874 m

Step-by-step explanation:

Given : The length and breadth of a room are 13m and 7.5m, respectively. the floor of the room is to be paved with square tiles of uniform size.

To find : Determine the length of the largest possible size of the tile?

Solution :

Length of room = 13m.

Breadth of room = 7.5m.

Area of the room is

$A=l\times b$

$A=13\times 7.5$

$A=97.5m^2$

Since the area of square is measured by squaring the sides.

So, we have to calculate the square root of the area

i.e, $s=\sqrt{97.5}$

$s=9.874m$

Therefore, if we consider integer value then a square tile can be of maximum 9 metres side.

Else if we consider the float value then it can be of 9.874 metres.