Rectangle-shaped 80074

Pupils had to stack rectangle-shaped pictures with dimensions of 210mm and 84mm so as to cover the square. What is the smallest square we can cover like this, and how many images do we need?

Correct answer:

a =  420 mm
n =  10

Step-by-step explanation:

$$\begin{gathered} x=210\text{mm} \\ y=84\text{mm} \\ 210=2\cdot 3\cdot 5\cdot 7 \\ 84=2^2\cdot 3\cdot 7 \\ LCM(210,84)=2^2\cdot 3\cdot 5\cdot 7=420 \\ a=LCM(x,y)=LCM(210,84)=420\text{mm} \end{gathered}$$

$$\begin{gathered} n=\frac{S_1}{S_2} \\ n=\frac{a\cdot a}{x\cdot y}=\frac{420\cdot 420}{210\cdot 84}=10 \end{gathered}$$

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