Garden fence

The quadrilateral garden should be fenced off with a slatted fence. The sides of the orchard are 65m, 78m, 40m and 32m. The wheels are to be placed 6m apart, and the axes of the rims are 15cm 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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