Bed 10

A bed in the shape of two equilateral triangles sharing a common side, with a side length of 2.5 m, is to be planted with seedlings of an ornamental shrub. The gardener recommended leaving 40 cm between individual seedlings and 10 cm from the perimeter edge for the outermost seedlings. Determine the maximum number of seedlings needed to plant this bed.

Final Answer:

n =  30

Step-by-step explanation:

$$\begin{gathered} a=2.5\text{m}\to \text{cm}=2.5\cdot 100\text{cm}=250\text{cm} \\ m=40\text{cm} \\ s=10\text{cm} \\ {a}_2=a-2\cdot s=250-2\cdot 10=230\text{cm} \\ {r}_1=\lfloor a_2/m\rfloor =\lfloor 230/40\rfloor =5 \\ {n}_1=r_1^2=5^2=25 \\ {m}_2=\sqrt{m^2-(m/2{)}^2}=\sqrt{40^2-(40/2{)}^2}=20\sqrt{3}\text{cm}\doteq 34.641\text{cm} \\ {r}_2=\lfloor a_2/m_2\rfloor =\lfloor 230/34.641\rfloor =6 \\ {n}_2=r_2\cdot r_1=6\cdot 5=30 \\ n=n_2=30 \end{gathered}$$

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