Paper

The drawing paper has dimensions 220 mm and 308 mm. Pupils should cut it into squares of the same size so that they are as large as possible. Determine the dimensions of the square in cm and the number of squares.

Final Answer:

a =  4.4 cm
n =  35

Step-by-step explanation:

$$\begin{gathered} x=220\text{mm} \\ y=308\text{mm} \\ 220=2^2\cdot 5\cdot 11 \\ 308=2^2\cdot 7\cdot 11 \\ \text{GCD}(220,308)=2^2\cdot 11=44 \\ A=GCD(x,y)=GCD(220,308)=44\text{mm} \\ a=A\to \text{cm}=A:10\text{cm}=44:10\text{cm}=4.4\text{cm}=4.4\text{cm} \end{gathered}$$

$$\begin{gathered} n_1=x/A=220/44=5 \\ {n}_2=y/A=308/44=7 \\ n=n_1\cdot n_2=5\cdot 7=35 \end{gathered}$$

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