length --- l
width ----w
2l+2w=36
l+w = 18
l = 18-w
area = lw = w(18-w) = 18w - w^2
d(area)/dw = 18-2w
= 0 for a max of area
2w = 18
w = 9
then l = 18-w = 9
so the area of the base of the box must be a square, 9 by 9
as you probably expected.
A rectangular box has a perimeter of 36 inches. Find the length and width of the box that would give the maximum area.
e. l = 9, w = 9
f. l = 81, w = 9
g. l = 27, w = 9
h. l = 18, w = 18
1 answer
1 answer