Question

The floor of a room is to be decorated with square tiles of length 6m. How many tiles are required if the floor of the room has dimensions $36m \times 24m$?

Answer 1

Hint – In this question the dimensions corresponds to the length and the breadth of the room that is length is 36m and the breadth is 24m so the area of the room that simply need to be covered with tiles will be the area of this room that is ${\text{length}} \times {\text{breadth}}$. Now the tile is of the square form so one side of the square is given and thus the area of the square can be calculated using formula ${(side)^2}$. Now the number of titles required to completely fill the floor of the room will be the fraction of the area of the room and that of the tile.

Complete step-by-step answer:
Given data:
The floor of a room is to be decorated with square tiles of length = 6m.
As the titles are in square shape so the area of the tiles is the square of the side length.
So the area of the square titles = ${\left( 6 \right)^2} = 36$ ${m}^{2}$.
Now the dimensions of the floor in which the tiles are planted is given as $36m \times 24m$
Now simplify this dimension value we have,
$ \Rightarrow 36m \times 24m = 864$ ${m}^{2}$.
Now the number of titles required to completely fill the floor of the room is the ratio of the dimension of the room in which tiles are planted to the area of the one tile.
So the number of titles required to completely fill the floor of the room = (dimension of the room/area of one tile).
Now substitute the values we have,
So the number of titles required to completely fill the floor of the room = $\dfrac{{864}}{{36}} = 24$.
So the number of tiles required to completely fill the floor is 24.
So this is the required answer.

Note – A rectangle has opposite sides equal so that how we can depict that the dimensions of the room given resembles that of a rectangle as one side is given as 36 and the other as 24 and these are different and only two sides are given, now for the tile part as the square has all four equal sides and thus the single dimension given depicts that it clearly is a square.