Determine 57151

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

Correct 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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