Fence posts

Mr. John's plot of land has dimensions of 252 dm and 28 m. How far apart must he place the fence posts so they are the same distance on both sides? How many will he need to fence the entire property?

Final Answer:

x =  28 dm
n =  38

Step-by-step explanation:

$$\begin{gathered} a=252\text{dm} \\ b=28\cdot 10=280\text{dm} \\ 252=2^2\cdot 3^2\cdot 7 \\ 280=2^3\cdot 5\cdot 7 \\ \text{GCD}(252,280)=2^2\cdot 7=28 \\ x=GCD(a,b)=GCD(252,280)=28\text{dm} \end{gathered}$$

$$\begin{gathered} o=2\cdot (a+b)=2\cdot (252+280)=1064\text{dm} \\ n=o/x=1064/28=38 \end{gathered}$$

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