Find the length and width of a rectangle that has the given area and a minimum perimeter.

Area: 50 square feet

1 answer

p = 2w + 2 L
L = 50/w
so
p = 2 w + 2 (50/w)

p = 2 ( w+50/w)

dp/dw = 0 at min or max

= 2 [ 1 - 50/w^2 ]

w^2 = 50
w = 5 sqrt 2
then
L = 50/[5 sqrt 2 ] = 10 srt 2/2
= 5 sqrt 2

LOL, it is square :)