Answer
The number of tiles needed to cover the rectangular floor is\[108\]
Work Step by Step
Firstly, convert each side of square tile from feet into inches as follows:
Sinceis equal to\[12\text{ inches}\], each side of the square in feet will be as follows:
\[\begin{align}
& \text{ 8 in}\text{.}=\frac{8\text{ in}}{1}\text{.}\times \frac{1\text{ ft}}{12\text{ in}} \\
& =\frac{8}{12}\text{ft}
\end{align}\]
In order to compute the number of tiles required for covering the floor. Firstly, compute the area of the square tile that will be computed by squaring the side of the tile. Secondly, compute the area of the rectangular floor that will be computed by multiplying the dimensions that are its length and breadth with each other.
Finally, compute, the number of tiles needed by dividing the area of rectangular floor with the area of 1 square tile.
Compute the area of the square tile using the equation as shown below:
\[\begin{align}
& \text{Area of 1 square tile}={{\text{s}}^{\text{2}}} \\
& ={{\left( \frac{8}{12}\text{ ft} \right)}^{2}} \\
& ={{\left( \frac{2}{3}\text{ ft} \right)}^{2}} \\
& =\frac{4}{9}\text{ f}{{\text{t}}^{\text{2}}}
\end{align}\]
Thus, the area of 1 square tile is \[\frac{4}{9}\text{ f}{{\text{t}}^{\text{2}}}\]
Now, compute the area of the rectangular floor using the equation as shown below:
\[\begin{align}
& \text{Area of the Rectangular floor (}A\text{)}=l\times b \\
& =\left( 8\text{ ft}\times 6\text{ ft} \right) \\
& =48\text{ f}{{\text{t}}^{\text{2}}}
\end{align}\]
Thus, the area of the triangle is \[48\text{ f}{{\text{t}}^{\text{2}}}\]
Now, compute the number of tiles needed to cover the floor using the equation as shown below:
\[\begin{align}
& \text{Number of tiles}=\frac{\text{Area of rectangular floor}}{\text{Area of 1 square tile}} \\
& =\frac{48\text{ f}{{\text{t}}^{\text{2}}}}{{4}/{9}\;\text{ f}{{\text{t}}^{\text{2}}}} \\
& =\frac{432}{4} \\
& =108
\end{align}\]
