Tiles

The room has dimensions of 12 m and 5.6 m. Determine the number of square tiles and their largest possible size to cover the room's floor.

Final Answer:

n =  105
x =  80 cm

Step-by-step explanation:

$$\begin{gathered} a=12\text{m}\to \text{cm}=12\cdot 100\text{cm}=1200\text{cm} \\ b=5.6\text{m}\to \text{cm}=5.6\cdot 100\text{cm}=560\text{cm} \\ 1200=2^4\cdot 3\cdot 5^2 \\ 560=2^4\cdot 5\cdot 7 \\ \text{GCD}(1200,560)=2^4\cdot 5=80 \\ x=GCD(a,b)=GCD(1200,560)=80 \\ n=\frac{a}{x}\cdot \frac{b}{x}=\frac{1200}{80}\cdot \frac{560}{80}=\frac{1200\cdot 560}{80\cdot 80}=\frac{672000}{6400}=105 \end{gathered}$$

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