Question

jamila keeps alpacas on a 1 - acre, square lot near her home. she has 8 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) 148 feet 296 feet 247 feet 362 feet

Explanation:

Step1: Calculate the side length of the square

Since the lot is square and 1 acre is 209 feet long (side - length of the square), let \(a = 209\) feet.

Step2: Use the Pythagorean theorem for the diagonal of a square

The formula for the diagonal \(d\) of a square with side - length \(a\) is \(d=\sqrt{a^{2}+a^{2}}=\sqrt{2a^{2}}=a\sqrt{2}\).
Substitute \(a = 209\) into the formula: \(d=209\sqrt{2}\).
We know that \(\sqrt{2}\approx1.414\), so \(d = 209\times1.414\).
\(209\times1.414=(200 + 9)\times1.414=200\times1.414+9\times1.414\).
\(200\times1.414 = 282.8\) and \(9\times1.414=12.726\).
Then \(d=282.8+12.726=295.526\approx296\) feet.

Answer:

296 feet