Garden

The garden has the shape of a rectangle measuring 19m20cm and 21m60cm. Mr. Novák will fence it. It wants the distance between adjacent pillars to be at least two meters and a maximum of three meters. He would also like the distances between the adjacent pillars to be the same on all sides. What is the distance between the pillars?

Result

x =  240 cm

Solution:

$a=19 \cdot \ 100+20=1920 \ \text{cm} \ \\ b=21 \cdot \ 100 + 60=2160 \ \text{cm} \ \\ 1920=2^7 \cdot 3 \cdot 5 \ \\ 2160=2^4 \cdot 3^3 \cdot 5 \ \\ \text{GCD}(1920, 2160)=2^4 \cdot 3 \cdot 5=240 \ \\ \ \\ s=GCD(a,b)=GCD(1920,2160)=240 \ \\ 200<x<300 \ \\ x=s=240 \ \text{cm}$

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