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?

Result

x =  20 cm
n =  57

Solution:

a=380 cm b=60 cm  380=2251960=2235GCD(380,60)=225=20  x=GCD(a,b)=GCD(380,60)=20=20  cm a = 380 \ cm \ \\ b = 60 \ 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 = 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 \ cm^2 \ \\ S_{ 2 } = x^2 = 20^2 = 400 \ cm^2 \ \\ \ \\ n = \dfrac{ S_{ 1 } }{ S_{ 2 } } = \dfrac{ 22800 }{ 400 } = 57



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