Rectangular flowerbed

Around the rectangular flowerbed with dimensions of 5.25 m and 3.50 m, roses should be planted at the same distance from each other so that they are located in each corner of the flower bed and consumed as little as possible. How far do we plant them? How many roses will we need?

Correct answer:

d =  175 cm
n =  10

Step-by-step explanation:

$$\begin{gathered} a=5.25\text{m}\to \text{cm}=5.25\cdot 100\text{cm}=525\text{cm} \\ b=3.50\text{m}\to \text{cm}=3.50\cdot 100\text{cm}=350\text{cm} \\ 525=3\cdot 5^2\cdot 7 \\ 350=2\cdot 5^2\cdot 7 \\ \text{GCD}(525,350)=5^2\cdot 7=175 \\ d=GCD(a,b)=GCD(525,350)=175\text{cm} \end{gathered}$$

$$\begin{gathered} o=2\cdot (a+b)=2\cdot (525+350)=1750 \\ n=o/d=1750/175=10 \end{gathered}$$

Try another example