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?

Question

247 feet
148 feet
296 feet
362 feet

Answer 1

To find the length of fencing that Jamila needs to split her square lot diagonally, we first need to determine the diagonal length of the lot.

1. Calculate the diagonal of the square lot: The formula for the diagonal \( d \) of a square with side length \( s \) is given by: \[ d = s \sqrt{2} \]

2. Determine the side length of the lot: Since 1 acre is equivalent to a square with each side being \( \sqrt{1 , \text{acre}} \), and given that 1 acre is \( 43,560 , \text{square feet} \), first calculate the side length: \[ s = \sqrt{43,560} \approx 209 , \text{feet} \]

3. Calculate the diagonal using the side length: Now we can plug in the side length into the diagonal formula: \[ d = 209 , \text{feet} \times \sqrt{2} \]

   Since \( \sqrt{2} \) is approximately \( 1.414 \): \[ d \approx 209 \times 1.414 \approx 295.652 , \text{feet} \]

4. Round the diagonal length to the nearest foot: Approximately, \( 295.652 \) feet rounds to \( 296 \) feet.

Therefore, the length of fencing that Jamila needs is 296 feet.