Jamila keeps alpacas on 1 acre square lot near her home. She has six alpacas and wants to build a fence diagonally to split the herd into if the acre is 209 feet long how many feet to the nearest foot of fencing does Jamila need?
Since Jamila wants to split the herd into two equal sections, she will need to build a fence diagonally across the acre. This diagonal will split the acre into two right triangles.
To find the length of the diagonal fence, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.
Let's denote the sides of the right triangle as follows:
- One side (a) is half the length of the acre, so a = 209 / 2 = 104.5 feet
- The other side (b) is the width of the acre, which is also 209 feet
- The hypotenuse (c) is the length of the diagonal fence we need to find
Using the Pythagorean theorem:
c^2 = a^2 + b^2
c^2 = 104.5^2 + 209^2
c^2 = 10902.25 + 43681
c^2 = 54583.25
Taking the square root of both sides to solve for c:
c = √54583.25
c ≈ 233.6 feet
Therefore, Jamila will need approximately 234 feet of fencing to build a diagonal fence to split her herd of alpacas.