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
