Answer:
The total area of the land is 4.4 square mi.
The length of the fence should be 9.2 mi.
Step-by-step explanation:
Consider the provided information.
The required figure is shown below:
First, we need to find the Hypotenuse of the triangle by using the Pythagoras theorem.
[tex](\text{Hyp})^2=(1.6)^2+(1.2)^2[/tex]
[tex](\text{Hyp})^2=2.56+1.44[/tex]
[tex](\text{Hyp})^2=4[/tex]
[tex]\text{Hyp}=2[/tex]
So, the hypotenuse of the triangle is 2 mi. Also, the hypotenuse of the triangle is the side of the rectangle.
Total area = Area of square + Area of Triangle + Area of rectangle
Total area = [tex]1.2\times 1.2+\frac{1}{2}(1.2)(1.6)+2\times 1[/tex]
Total area = [tex]1.44+0.96+ 2[/tex]
Total area = 4.4 square mi.
Now calculate the fencing they need to enclose the outside of their farm.
For this add the length of the red lines shown in the figure below:
[tex]\text{Fence length outside the farm}=1.2+1.6+1+2+1+1.2+1.2[/tex]
[tex]\text{Fence length outside the farm}=9.2[/tex]
Hence, the length of the fence should be 9.2 mi.
