Question

rectangular room 3.30m by 5.25 m is
to be paved with square tiles of the
same size. Find the largest size of a square tile
and the number of
tiles
that will be needed.​

Answer 1

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Answer 2

Answer:

Largest size of a square tile = 225 cm.

$\large \text{Number of tiles = 770 }$

Step-by-step explanation:

Given :

Length and breadth of rectangular room is 5.25 m and 3.30 m .

Area of rectangular room =  Length × breadth

Area of rectangular room = 5.25 × 3.30 = 17.325 $m^2$ or 1,73,250 $cm^2$

Largest size of a square tile = H.C.F. ( 525 and 330 )

H.C.F. ( 525 and 330 )

525 = 330 × 1 + 195

330 = 195 × 1 + 135

195 = 135 × 1 + 60

135 = 60 × 2 + 15

60 = 15 × 4 + 0

So H.C.F. ( 525 and 330 ) = 15

It is side of square tile .

Area of square tile = side × side

Area of square tile = 15 × 15 = 225 $cm^2$

Now  the number of  tiles  that will be needed =

$\large \dfrac{Area \ of \ rectangular \ room }{Area \ of \ one \ tiles}$

$\large \text{Number of tiles = \dfrac{1,73,250}{225} }\\\\\\\large \text{Number of tiles = 770 }$