Question

Samyak wants to cover the floor of a room 3m wide and 4m long with square tiles. If each tile is of the side 0.5m, then find the number of tiles required to cover the floor of the room.

Answer 1

Hint: We have a room whose floor needs to be covered with squared tiles. First, we will find the area of the floor using the formula, \[\text{Area}=L\times B.\] Then we will find the area of one square tile using the formula, \[\text{Area}={{\left( \text{side} \right)}^{2}}.\] Then we will assume that n tiles will be needed in total. So, this will give, \[n\times \text{Area of 1 tile}=\text{Area of the floor}\text{.}\] So we will put those values and find the value of n. This n will give us our required solution.

Complete step by step answer:
We are given that the floor of the room has length 3m wide and 4m long. So, it is a rectangular room and needs to cover its floor with square tiles of 0.5m.

First, we will find the area of the whole floor and the area of one file. Now, the room is a rectangular box with L as 4m and B as 3m. We know that the area of the rectangle is given as \[\text{Area}=L\times B.\]
So, the area of the floor of the room will be,
\[\text{Area of the floor of room}=3\times 4=12{{m}^{2}}\]
Now, one tile is in the square shape. The area of the square is given as, \[\text{Area}=\left( \text{side} \right)\times \left( \text{side} \right).\] As the side of the tile is 0.5m, we get,
\[\text{Area of 1 tile}=0.5\times 0.5=0.25{{m}^{2}}\]
Let us assume ‘n’ number of such tiles is needed. So, n tiles will cover the floor, it means that
n tiles Area = Area of rectangular floor
Now, as the area of 1 tile is \[0.25{{m}^{2}}\] using the unitary method, we get,
\[\text{Area of n tile}=n\times 0.25{{m}^{2}}\]
\[\Rightarrow \text{Area of n tile}=0.25n\text{ }{{m}^{2}}\]
Now, the area of n tiles = Area of the floor.
\[\Rightarrow 0.25n=12\]
Simplifying further, we get,
\[\Rightarrow n=\dfrac{12}{0.25}\]
\[\Rightarrow n=48\]

So a total of 48 tiles are needed.

Note: Remember that when we multiply variables with a constant, the variable gets attached at the last term.
\[\text{Area of n tile}=n\times 0.25{{m}^{2}}\]
\[\Rightarrow \text{Area of n tile}=0.25n\text{ }{{m}^{2}}\]
Remember that, \[n\times 0.25\ne 0.25+n.\] For any calculation, \[\dfrac{12}{0.25}\] we cancel the decimal by multiplying by 100 above. So, we get,
\[\Rightarrow \dfrac{12}{0.25}=\dfrac{12\times 100}{25}\]
On simplifying we get,
\[\Rightarrow \dfrac{12}{0.25}=48\]