Plumber

The plumber had to cut the metal strip with dimensions of 380 cm and 60 cm to the largest squares to no waste. Calculate the length of the sides of a square. How many squares cut it?

Correct answer:

x =  20 cm
n =  57

Step-by-step explanation:

$$\begin{gathered} a=380\text{cm} \\ b=60\text{cm} \\ 380=2^2\cdot 5\cdot 19 \\ 60=2^2\cdot 3\cdot 5 \\ \text{GCD}(380,60)=2^2\cdot 5=20 \\ x=GCD(a,b)=GCD(380,60)=20\text{cm} \end{gathered}$$

$$\begin{gathered} S_1=a\cdot b=380\cdot 60=22800{\text{cm}}^2 \\ {S}_2=x^2=20^2=400{\text{cm}}^2 \\ n=\frac{S_1}{S_2}=\frac{22800}{400}=57 \end{gathered}$$

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