Diameters of euro coins

When paying, we use euro coins with the following diameters:
The 10-cent coin has a diameter of 19.75 mm.
The 20-cent coin has a diameter of 22.25 mm.
The 50-cent coin has a diameter of 24.25 mm.
Find out in what ratio the diameters of these coins are.

Final Answer:

r = 79:89:97

Step-by-step explanation:

$$\begin{gathered} d_1=19.75\cdot 100=1975 \\ {d}_2=22.25\cdot 100=2225 \\ {d}_3=24.25\cdot 100=2425 \\ 1975=5^2\cdot 79 \\ 2225=5^2\cdot 89 \\ 2425=5^2\cdot 97 \\ \text{GCD}(1975,2225,2425)=5^2=25 \\ x=GCD(d_1,d_2,d_3)=GCD(1975,2225,2425)=25 \\ {p}_1=d_1/x=1975/25=79 \\ {p}_2=d_2/x=2225/25=89 \\ {p}_3=d_3/x=2425/25=97 \\ r=79:89:97 \end{gathered}$$

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