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?

Correct result:

x =  240 cm

Solution:

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

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