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 herd in two.

If an acre is 209 feet long, how many feet, to the nearest foot, of fencing does Jamila need?

(1 point)
Responses

362 feet
362 feet

247 feet
247 feet

296 feet
296 feet

148 feet

1 answer

To determine how much fencing Jamila needs to split her 1-acre square lot diagonally, we first need to calculate the length of the diagonal of the square.

Since the lot is a square and each side is 209 feet long, we can use the Pythagorean theorem to find the length of the diagonal \(d\):

\[ d = \sqrt{side^2 + side^2} = \sqrt{209^2 + 209^2} = \sqrt{2 \cdot 209^2} = 209\sqrt{2} \]

Now we calculate \(209\sqrt{2}\): \[ \sqrt{2} \approx 1.414 \]

Therefore: \[ d \approx 209 \times 1.414 \approx 295.806 \]

Rounding \(295.806\) to the nearest foot, we get \(296\) feet.

Thus, Jamila needs 296 feet of fencing.