Question

Floor tiles are 25 cm squares. How many tiles will be needed for a rectangle lawn 12 m long and 10 m wide. Find the cost at the rate of Rs. 8 per tile?

Answer 1

Hint: Here in this question we have to find the number of tiles required for the rectangular lawn of length 12 m and the breadth 10 m. By using the area formula, first we determine the area of the rectangular lawn and then we determine how many tiles are needed to cover the rectangular lawn after this we determine the total cost.

Complete step by step solution:
In the question we have floor tiles that are 25 cm squares. Therefore the area of each tile is 25 cm squares.
The length of rectangular lawn is 12 m
The breadth of the rectangular lawn is 10 m
The area of the rectangular lawn is \[l \times b\]. Therefore on substituting the value of length and breadth we have
\[ \Rightarrow A = l \times b = 12 \times 10\]
On simplifying
\[ \Rightarrow 120\] m squares.
The number of tiles required for the rectangular lawn is the ratio of the area of the rectangular lawn to the area of a tile.
number of tiles = \[\dfrac{{{\text{area of rectangular lawn}}}}{{{\text{area of tile}}}}\]
Substituting the values to the above formula. since the area of rectangular lawn is in the metre square and the area of tile is in the centimetre square. So let us convert the area of tile to the unit to metre.
number of tiles = \[\dfrac{{120}}{{25 \times {{10}^{ - 4}}}}\]
\[
   \Rightarrow \dfrac{{120 \times {{10}^4}}}{{25}} \\
   \Rightarrow 48000 \\
 \]
Therefore the number of tiles is 48,000.
The cost of one tile is Rs.8
Therefore the cost of 48,000 tiles is \[8 \times 48000\]
On simplifying we have
\[ \Rightarrow 384000\]
Therefore the total cost is Rs. 3,84,000

Note: The problem is related to the area of a rectangular quantity. Then it is extended to determine the total cost for the tiles. While dividing the quantities the units should be in the same unit. If the units are different then we have to convert any one of the quantities to the quantity of the another.