Jamila keeps alpacas on a 1-acre, square lot near her home. She has 6 alpacas and wants to build a fence diagonally to split the herdin two. If an acre is 209 feet long, how many feet, to the nearest foot, of fencing does Jamila need?

Answer 1

To determine how much fencing Jamila needs to build a diagonal fence that splits her 1-acre square lot into two equal halves, we first need to find the length of the diagonal of the square.

1. Understanding the square lot:
   Since the area of the lot is 1 acre, and 1 acre is defined as 43,560 square feet, we will calculate the side length of the square lot. Using the formula for the area of a square (Area = side²):

   \[ \text{side} = \sqrt{\text{Area}} = \sqrt{43560} \]

   Calculating this gives:

   \[ \text{side} \approx 208.71 \text{ feet} \]

2. Finding the diagonal length:
   The formula for the diagonal \(d\) of a square is given by:

   \[ d = \text{side} \times \sqrt{2} \]

   Substituting the side length we computed:

   \[ d \approx 208.71 \times \sqrt{2} \]

   Now calculating \(\sqrt{2} \approx 1.414\):

   \[ d \approx 208.71 \times 1.414 \approx 295.56 \text{ feet} \]

3. Rounding to the nearest foot:
   To find out how much fencing Jamila needs, we round \(295.56\) to the nearest foot:

   \[ d \approx 296 \text{ feet} \]

Therefore, the amount of fencing Jamila needs is:

\[ \boxed{296} \text{ feet} \]