Question

The rancher needs to replace the fence for the holding

pen for the horses. How much fencing does he need?

Answer 1

To calculate the amount of fencing needed for a holding pen, one must know the pen's dimensions. For simple shapes like rectangles or triangles, summing the lengths of the sides or employing geometric principles like the law of cosines would yield the required fence length. Complex shapes or additional features may complicate the calculation.

Step-by-step explanation:

Calculating the Fencing Needed for Land

To determine how much fencing a rancher needs for a holding pen, one must know the dimensions of the area being fenced. For example, for a rectangular pen, you would add together the lengths of all four sides. However, the complexity of the problem can increase if the shape is irregular or if there are specific features like gates or pre-existing structures that would reduce the amount of fencing material needed.

In the case of a triangular piece of land, as mentioned in question 20, with two sides being 80.0 m and 105 m long, to find the length and orientation of the third side C, one would typically use the law of cosines if the angle between sides A and B were known. For land plots with different polygons or complex shapes, different formulas would apply based on geometric principles.

The historical context and the impact of different fencing types mentioned in the additional information provided, like the Running Fence by Christo and Jeanne-Claude, can illustrate real-world applications and economic considerations, but are not directly needed for the calculations of fencing required for a holding pen.

Answer 2

To determine how much fencing the rancher needs to replace the fence for the holding pen for the horses, we need to know the perimeter of the holding pen. If we assume that the holding pen is rectangular, we can use the formula for the perimeter of a rectangle:

P = 2L + 2W

where P is the perimeter, L is the length, and W is the width of the rectangle. If we know the length and width of the holding pen, we can plug in the values and solve for the perimeter.

For example, if the length of the holding pen is 50 meters and the width is 30 meters, we can calculate the perimeter as follows:

P = 2L + 2W = 2(50 m) + 2(30 m) = 100 m + 60 m = 160 m

Therefore, the rancher needs 160 meters of fencing to replace the fence for the holding pen for the horses.