Engineering

4. A rectangular enclosure is formed by using 800m of fencing. Find the greatest possible area that can be enclosed in this way and the corresponding dimensions of the rectangle.

asked by Alexander
  1. 4 x = 800
    x = 200 feet on a side square

    =========================
    prove that square is max area

    A = x y
    P = 2 x + 2 y perimeter
    so x + y = P/2
    A = x (P/2 - x) = -x^2 +P/2 x

    x^2 - (P/2) x = A find vertex,complete square
    x^2 - (P/2)x + P^2/16 = -A + P^2/16

    (x-P/4)^2 = -(A-P^2/16)

    vertex at x= P/4 (then y = P/4 too :)
    A = (P/4)^2
    so square with side = Perimeter/4 is max area

    posted by Damon

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