An architect is designing an atrium for a hotel. The Atrium is to be rectangular with a perimeter of 728ft of brass piping. What dimensions will maximize the area of the atrium?

asked by Ethan
  1. p = 2 L + 2 w = 728 so L + w = 364 and L = (364-w)
    A = L w

    A = (364-w)w = 364 w - w^2
    dA/dw = 0 at max or min = 364 -2w
    w = 182
    L = 364-w = 182
    LOL, a square
    or if you do not know calculus
    w^2 - 364 w = -A
    complete square to find vertex
    w^2 - 364 w + (182)^2 = -A+182^2
    (w-182)^2 = -A+182^2
    vertex at w = 182 again

    posted by Damon

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