Tiles

The hall has dimensions 250 × 200 dm. What is the largest size of square tiles that can be tiled throughout the hall, and how many do we need?

Final Answer:

x =  50 dm
y =  50 dm
n =  20

Step-by-step explanation:

$$\begin{gathered} A=250\text{dm} \\ B=200\text{dm} \\ 250=2\cdot 5^3 \\ 200=2^3\cdot 5^2 \\ \text{GCD}(250,200)=2\cdot 5^2=50 \\ x=GCD(A,B)=GCD(250,200)=50\text{dm} \end{gathered}$$

$y=x=50=50\text{dm}$

$$\begin{gathered} S_1=A\cdot B=250\cdot 200=50000{\text{dm}}^2 \\ {S}_2=x\cdot y=50\cdot 50=2500{\text{dm}}^2 \\ n=S_1/S_2=50000/2500=20 \end{gathered}$$

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