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 :)
Find the length and width of a rectangle that has the given area and a minimum perimeter.
Area: 50 square feet
1 answer