Van has 120 feet of fence to make a rectangular pen for his rabbits. If a shed is used as one side of the pen, what would the length and width be for maximum area? ( Only three sides are enclosed.)

Thus the dimensions to maximize the area is 30 by 60

Step-by-step explanation:

Let x= the length of the side perpendicular to the pen

and 120-2x= length of the side parallel to the shed

Area = x (120-2x) (1)

Area =120x - 2

The formula for the w-value of maximum is: -b/2a, thus our value will be:

-120/(-4) = 30

and substitue x = 30 into (1), we have:  120-2(30) =60

Thus the dimensions to maximize the area is 30 by 60

the first one, all those points on the line just make a strait line.