Given the area of a rectangle is A = bh, and assuming the rectangle is open on one side, perimeter b + 2h = 40, what formula will maximize the area of the rectangle

1 answer

rectangle open on one side ??

Poor wording, I will assume that this is the "classic" problem where you have perimeter on only 3 sides, such as the rectangle is against a building.

b = 40 - 2h

A = bh
= h(40-2h)
= -2h^2 + 40h

dA/dh = -4h + 40
= 0 for a max of A
4h=40
h = 10
b = 40-20 = 20

The maximum area is 10(20) or 200 units^2