Mathematics

Question

Bryan has a square parcel of land that is 120 yards long and 120 yards wide. The land is planted with Bermuda grass and surrounded by a fence. So that his cattle will not ruin the grass, Bryan decides to split the field into two halves and rotate his cattle on the land every 30 days. He plans to build a fence diagonally across the field. How many feet of fencing will Bryan need to split the parcel of land in half? Round your answer to the nearest yard.

2 Answer

  • You are basically finding the hypotenuse of a triangle with side lengths of 120 yards and 120 yards.
    Using the equation a^2 + b^2 = c^2, solve for c (hypotenuse) where a and b are the side lengths (120 yards).

    a^2 + b^2 = c^2
    square root(a^2 + b^2) = c
    square root (120^2 + 120^2) = c
    square root (120^2 + 120^2) = c
    square root (14400 + 14400) =c
    square root (28800) = 169.7, rounded up to 170 yards of fencing needed.
  • Answer:

    170

    Since the length of the fencing is equal to the diagonal of the square, or the hypotenuse for each of the triangles

    Equation:

    [tex]\left[\begin{array}{ccc}Hypotenuse =\sqrt{120^{2}+120^{2}} \neq 170\end{array}\right][/tex]

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