Triangle land fencing

The land has the shape of an obtuse triangle with sides of 40 m, 30, and 60 m. Determine the minimum mesh length for fencing and the land area in ares.

Final Answer:

x =  130 m
S =  5.3327 a

Step-by-step explanation:

$$\begin{gathered} a=40\text{m} \\ b=30\text{m} \\ c=60\text{m} \\ x=a+b+c=40+30+60=130\text{m} \end{gathered}$$

$$\begin{gathered} s=\frac{x}{2}=\frac{130}{2}=65\text{m} \\ {S}_1=\sqrt{s\cdot (s-a)\cdot (s-b)\cdot (s-c)}=\sqrt{65\cdot (65-40)\cdot (65-30)\cdot (65-60)}=25\sqrt{455}{\text{m}}^2\doteq 533.2682{\text{m}}^2 \\ S=S_1\to \text{a}=S_1:100\text{a}=533.2682:100\text{a}=5.333\text{a}=5.3327\text{a} \end{gathered}$$

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