Floor of a square room of side 10 m is to be completely covered with square tiles, each having length 50 cm. Find the smallest number of tiles needed ?

The correct answer is: ∴ A minimum of 400 tiles are required to cover the room.

Step-by-step solution:-
Covering the floor of a room with tiles means putting tiles on the whole surface of the room.
∴ If we know the area of the whole room and the area of each tile, we can find the number of tiles required to cover the floor.
Let the number of tiles required be n
Now, from the given information,
Side of the room = S1 = 10 m ............................................................................................. (Equation i)
Side of each tile = S2 = 50 cm = 0.5 m ............................................... (1m = 100 cm) ............ (Equation ii)
∴ Area of the room = Side 1 ²
∴ Area of the room = 10² ................................................................. (From Equation i)
∴ Area of the room = 100 m² ............................................................... (Equation iii)
Area of each tile = Side 2 ²
∴ Area of each tile = 0.5² .................................................................................... (From Equation ii)
∴ Area of each tile = 0.25 m² ............................................................... (Equation iv)
Area of the room = Area of each tile × total number of tiles required.
∴                   100 = 0.25 × total number of tiles required ................... (From Equations iii & iv)
∴         100 / 0.25 = total number of tiles required
∴                   400 = total number of tiles required
Final Answer:-
∴ A minimum of 400 tiles are required to cover the room.