Notice that both regions are right triangles.
As for Grassland, its area is given by the formula:
[tex]\begin{gathered} A_G=\frac{1}{2}bh,A_G=2400 \\ \Rightarrow\frac{1}{2}bh=2400 \\ \Rightarrow b=\frac{4800}{h}=\frac{4800}{60}=80 \\ \Rightarrow b=80 \end{gathered}[/tex]
Then, the base of Grassland is equal to 80.
Furthermore, we can use the Pythagorean theorem to find the value of its hypotenuse:
[tex]\text{hypotenuse}=\sqrt[]{80^2+60^2}=100[/tex]
With this, we have found all the sides of the Grassland triangle, which is:
And the Forest triangle is similar to the Grassland triangle; then, their corresponding sides have the same ratio
Consider the diagram:
Then, due to the similarity between the triangles:
[tex]\begin{gathered} \frac{45}{60}=\frac{x}{80} \\ \Rightarrow x=80\cdot\frac{45}{60}=60 \end{gathered}[/tex]
And
[tex]\begin{gathered} \frac{45}{60}=\frac{y}{100} \\ \Rightarrow y=\frac{4500}{60}=75 \end{gathered}[/tex]
Then, the Forest triangle is:
a) The perimeter of the Forest triangle is
[tex]\begin{gathered} P_F=45+75+60=180yd \\ \Rightarrow P_F=180\cdot3=540ft \end{gathered}[/tex]
540ft, and, since the fence is $6 per foot, we need
[tex]540\cdot6=3240[/tex]
$3240 to surround the whole Forest triangle.
b)
