Question

The floor of a room is in the shape of a square of side 4.8m. The floor is to be covered with square tiles of perimeter 1.2 m. Find the cost of covering the floor if each tile costs ₹27.

Answer 1

Hint: Perimeter is defined as the boundary of a geometrical figure formed by a continuous line. The area of a figure is defined as the amount of space inside the boundaries of a two-dimensional figure or the surface of a three-dimensional object. From the perimeter of the tiles, we can find out the length of its side and thus its area. Dividing the area of the floor by the area of one tile, we can find out the number of tiles and hence the cost of covering the floor with tiles.

Complete step-by-step answer:
We are given that the side of the square floor is 4.8m long, so the area of the floor is
 $ \Rightarrow A = {(side)^2} = 4.8 \times 4.8 = 23.04\;{m^2} $
Now, the perimeter of the square tile is 1.2m, we know that $ perimeter = 4(side) $
So the length of its side is
 $ \Rightarrow side = \dfrac{{perimeter}}{4} = \dfrac{{1.2}}{4} = 0.3\;m $
The area of one tile is $ A = {(0.3)^2} = 0.09\;{m^2} $
So the number of tiles,
 $ \Rightarrow n = \dfrac{{area\,of\,floor}}{{area\,of\,one\,tile}} = \dfrac{{23.04}}{{0.09}} = 256 $
Cost of one tile = ₹27
Cost of 256 tiles = ₹6912
Hence the cost of covering the floor is ₹6912.
So, the correct answer is “ ₹6912”.

Note: The magnitude of the perimeter is the length of this boundary. The perimeter of different figures is calculated by different formulas; it is simply the sum of all the sides present in the figure.
The square has four sides so its $ perimeter = side + side + side + side = 4 \times side $ .
The area of a figure is equal to the product of its height and the width. As the width of the square is equal to its height, so the area of the square is given as, $ area = side \times side = {(side)^2} $ .