Question

A room is 11.5 m long and 6.3 m wide. Its floor is to be covered with rectangle tiles of size 23 cm by 9 cm. Find the total cost of tiling the floor at the rate of Rs. 4.25 per tile.
A. Rs. 15725
B. Rs. 14800
C. Rs. 16795
D. Rs. 14875

Answer 1

Hint:
 A rectangle is a 2D-shape which has four sides and four vertices. All the four angles of the rectangle are right angles. The opposite sides of the rectangle are equal and parallel to each other. The area of the rectangle depends on its sides. Basically, the formula for area is equal to the product of length and breadth of the rectangle.
Area of rectangle = (Length) × (Breadth)
To solve this question we need to calculate the area of the floor first, and we also know the dimensions of tile so we can calculate its area also. Now to calculate the total costing of tiling of the floor we need to find the number of tiles required to cover the floor completely. To find the number of tiles we divide the area of the floor by the area of one tile and then the total number of tiles is multiplied by the cost of one tile to get the total costing of the tiling.

Complete step by step solution:
It is given that,
[1m = 100cm]
Length of the room = 11.5m =1150cm
Breadth of the room = 6.3m = 630cm
As floor of the room is in the shape of rectangle, therefore we will calculate the area of the floor
Area of the floor = (Length) × (Breadth)
Area = $1150 \times 630 = 724500sq.cm$
Dimension of the tile = 23cm by 9cm
Area of 1 tile = $23 \times 9 = 207sq.cm$
To calculate the number of tiles,
$\begin{gathered}
  {\text{Number of tiles required = }}\dfrac{{{\text{Area of floor}}}}{{{\text{Area of tile}}}} \\
   = \dfrac{{724500}}{{207}} \\
   = 3500 \\
\end{gathered} $
Therefore, the total numbers of tiles required are 3500.
Now, to calculate the total cost of tiling
Cost of 1 tile = Rs.4.25
Total cost of tiling = $\left( {{\text{Number of tiles}}} \right)\times \left( {{\text{Cost of 1 tile}}} \right)$
$ = 3500 \times 4.25 = 14875$
Hence, the total cost of tiling the floor is Rs. 14875
∴Option (D) is correct.

Note:
To find the area with the diagonal of rectangle and breadth we use the formula,
${\text{Area = Breadth}}\sqrt {\left( {{\text{Diagona}}{{\text{l}}^{\text{2}}}{\text{ - Breadt}}{{\text{h}}^{\text{2}}}} \right)} $
And when we have to find the length or breadth when area is given,
${\text{Length = }}\dfrac{{{\text{Area}}}}{{{\text{Breadth}}}}$