SOLUTION: what is the largest rectangular area that can be enclosed with 16 meters of fence?

Question 865856: what is the largest rectangular area that can be enclosed with 16 meters of fence?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
what is the largest rectangular area that can be enclosed with 16 meters of fence?
Let L = length
and W = width
.
2(L + W) = 16 (equation 1)
area = WL (equation 2)
.
Solve equation 1 for L:
2(L + W) = 16
(L + W) = 8
L = 8-W
.
Substitute above into equation 2:
area = W(8-W)
area = 8W-W^2
area = -W^2+8W
this is a quadratic (parabola) that opens downwards (from the negative coefficient associated with the W^2 term). This means the vertex is the Max.
max is at
W = -b/(2a)
W = -8/(2*(-1))
W = -8/(-2)
W = 4 meters (width)
.
L = 8-W = 8-4 = 4 meters (length)
.
Maximum area is
WL = 4*4 = 16 square meters

RELATED QUESTIONS
A farmer has 230 ft of fence to enclose a rectangular garden. What is the largest garden... (answered by edjones)

Farmer Ed has 4,000 meters of fencing, and wants to enclose a rectangular plot that... (answered by macston)

The Maximum Garden Problem. A farmer has 230 ft of fence to enclose a rectangular... (answered by drk)

What is the largest rectangular area that can be enclosed with 30 feet of fencing? I need (answered by fractalier)

A farmer with 1000 meters of fencing wants to enclose a rectangular plot that borders... (answered by KMST)

a farmer with 4000 meters of fencing wants to encloce a rectangular plot that borders on... (answered by checkley77)

Farmer Ed has 3,000 meters of fencing, and wants to enclose a rectangular plot that... (answered by Boreal)

Enclosing the Most Area with a Fence. A farmer with 4000 meters of fencing wants to... (answered by checkley77)

A developer wants to enclose a rectangular lot that borders a city street. If the... (answered by bucky)