Trigo Problem

[Guest]

A triangular plot measures 20 m, 25 m, and 30 m respectively. A goat is teetered to stake within the plot. Find the minimum length of rope so that the goat can graze on the entire plot.

[Baltuilhe]

Good night!

Calculating the area:
First, the semiperimeter:
[tex]p=\frac{20+25+30}{2}=\frac{75}{2}=37,5[/tex]

Now, using Heron's Formula:
[tex]A=\sqrt{p(p-a)(p-b)(p-c)}=\sqrt{37,5(37,5-20)(37,5-25)(37,5-30)}=\sqrt{37,5\cdot 17,5\cdot 12,5\cdot 7,5}\Rightarrow A\approx 248,04[/tex]

Now, we have the area, we can use it to calculate the radius of external circle.
[tex]A=\frac{abc}{4R}=\frac{20\cdot 25\cdot 30}{4R}\approx 248,04\\\\\\
R\approx\frac{20\cdot 25\cdot 30}{4\cdot 248,04}\\\\\\
R\approx 15,12m[/tex]

So, the minimum lenght of rope is 15,12m, put in the circumcenter of the triangle

Hope to have helped!