Question

Raphael has an odd-shaped field shown in Figure 13-2. He wants to put a four-strand barbed wire fence around it for his cattle.A. What is the perimeter of the field?b. How many 80-rod rolls of barbed wire does he need topurchase?c. How many acres will be fenced?

Answer 1

Answer: Total perimeter = 9, 962.01 feet

The figure is a composite structure

It contains a rectangle and triangle

The perimeter of a rectangle is given as

Perimeter = 2( length + width)

length of the rectangle = 1500ft

Width of the rectangle = 1390 ft

Perimeter = 2( 1500 + 1390)

Perimeter = 2(2890)

Perimeter = 5780 ft

To calculate the perimeter of a triangle

`\begin{gathered} \text{Perimeter = a + b + }\sqrt[]{a^2+b^2} \\ a\text{ = 1050ft and b = 1390 ft} \\ \text{Perimeter = 1050 + 1390 + }\sqrt[]{1050^2+1390^2} \\ \text{Perimeter = 2440 + }\sqrt[]{1,102,\text{ 500 + 1, 932, 100}} \\ \text{Perimeter = 2400 + }\sqrt[]{3,034,600} \\ \text{Perimeter = 2440 + 1,742,01} \\ \text{Perimeter = }4182.01\text{ f}eet \end{gathered}`

The total perimeter of the field = Perimeter of the rectangle + perimeter of the right triangle

Total perimeter = 5780 + 4182.01

Total perimeter = 9, 962.01 feet