Jamila keeps alpacas on 1-acre, square lot near her home.

Question

she has 6 alpacas and wants to build a fence diagonally to split the herd in two.
If an acre is 209 feet long, how many feet, to the nearest foot, of fencing does jamila need?

247 feet
296 feet
362 feet
148 feet

Answer 1

To determine how much fencing Jamila needs to build a fence diagonally across a square lot, we first need to find the length of the diagonal of the square.

Given that 1 acre is represented as a square lot, and each side of the square is 209 feet, we can use the Pythagorean theorem to find the diagonal length \(d\) of the square. The formula for the diagonal \(d\) of a square with side length \(s\) is:

\[ d = s \sqrt{2} \]

In this case, the side length \(s\) is 209 feet. Plugging in the values:

\[ d = 209 \cdot \sqrt{2} \]

To calculate \(\sqrt{2}\):

\[ \sqrt{2} \approx 1.414 \]

Now substituting this value:

\[ d \approx 209 \cdot 1.414 \approx 295.506 \]

Rounding this to the nearest foot gives approximately 296 feet.

Thus, the amount of fencing Jamila needs is:

296 feet.

Answer 2

u sure

Answer 3

Let me double-check the calculations for clarity:

1. Finding the diagonal of a square lot: The formula for the diagonal \(d\) of a square with side length \(s\) is:

   \[ d = s \sqrt{2} \]

   Given that the side length \(s\) is 209 feet:

   \[ d = 209 \cdot \sqrt{2} \]

2. Calculating \(\sqrt{2}\): The approximate value of \(\sqrt{2}\) is about 1.414.

3. Calculating the diagonal:

   \[ d \approx 209 \cdot 1.414 \approx 295.506 \]

   Rounding 295.506 to the nearest foot gives us 296 feet.

So, the answer remains 296 feet for the amount of fencing needed. Thank you for your patience, and it looks like the calculations are indeed correct!