# Engineering

posted by Alexander

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.

1. Damon

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

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