Square plot paving

We will pave a square plot of land from rectangular tiles with 25 cm and 30 cm dimensions. What is the smallest square plot we can pave with these tiles without cutting them?

Final Answer:

a =  1.5 m
S =  2.25 m²

Step-by-step explanation:

$$\begin{gathered} x=25\text{cm} \\ y=30\text{cm} \\ 25=5^2 \\ 30=2\cdot 3\cdot 5 \\ LCM(25,30)=2\cdot 3\cdot 5^2=150 \\ z=LCM(x,y)=LCM(25,30)=150 \\ a=z\to \text{m}=z:100\text{m}=150:100\text{m}=1.5\text{m}=1.5\text{m} \end{gathered}$$

$S=a^2=1.5^2=2.25{\text{m}}^2$

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