# Math

posted by Ethan

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?

1. Damon

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
so
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

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