Paper

The drawing paper has dimensions 220mm and 308mm. 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.

Correct 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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