Garden fence

The quadrilateral garden should be fenced off with a slatted fence. The sides of the orchard are 65 m, 78 m, 40 m and 32 m. The wheels are to be placed 6 m apart, and the axes of the rims are 15 cm apart. How much is needed for a wheel fence, and how many battens are nailed when one batten is cut into 3 holes?

Final Answer:

k =  33
l =  478

Step-by-step explanation:

$$\begin{gathered} a=65 \\ b=78 \\ c=40 \\ d=32 \\ {k}_1=\lceil a/6\rceil =\lceil 65/6\rceil =11 \\ {k}_2=\lceil b/6\rceil -1=\lceil 78/6\rceil -1=12 \\ {k}_3=\lceil c/6\rceil -1=\lceil 40/6\rceil -1=6 \\ {k}_4=\lceil d/6\rceil -2=\lceil 32/6\rceil -2=4 \\ k=k_1+k_2+k_3+k_4=11+12+6+4=33 \end{gathered}$$

$$\begin{gathered} s=(a+b+c+d)/0.15=(65+78+40+32)/0.15=\frac{4300}{3}=1433\frac{1}{3}\doteq 1433.3333 \\ l=\lceil s/3\rceil =\lceil 1433.3333/3\rceil =478 \end{gathered}$$

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