Plumber

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

Correct result:

x =  20 cm
n =  57

Solution:

a=380 cm b=60 cm  380=22519 60=2235 GCD(380,60)=225=20  x=GCD(a,b)=GCD(380,60)=20 cma=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}
S1=a b=380 60=22800 cm2 S2=x2=202=400 cm2  n=S1S2=22800400=57S_{1}=a \cdot \ b=380 \cdot \ 60=22800 \ \text{cm}^2 \ \\ S_{2}=x^2=20^2=400 \ \text{cm}^2 \ \\ \ \\ n=\dfrac{ S_{1} }{ S_{2} }=\dfrac{ 22800 }{ 400 }=57



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