Around the flowerbed

Roses are to be planted equally spaced around a rectangular flowerbed with dimensions 5.25 m and 9.0 m so that they are found in every corner of the flowerbed and consumed as little as possible.

a) At what distance are planted roses?
b) How many roses do you need?

Final Answer:

d =  75 cm
n =  38

Step-by-step explanation:

$$\begin{gathered} a=5.25\text{m}\to \text{cm}=5.25\cdot 100\text{cm}=525\text{cm} \\ b=9.0\text{m}\to \text{cm}=9.0\cdot 100\text{cm}=900\text{cm} \\ 525=3\cdot 5^2\cdot 7 \\ 900=2^2\cdot 3^2\cdot 5^2 \\ \text{GCD}(525,900)=3\cdot 5^2=75 \\ d=GCD(a,b)=GCD(525,900)=75\text{cm} \end{gathered}$$

$$\begin{gathered} o=2\cdot (a+b)=2\cdot (525+900)=2850\text{cm} \\ n=\frac{o}{d}=\frac{2850}{75}=38 \end{gathered}$$

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