A 384 square meter plot of land is to be enclosed by a fence and divided into equal parts by a fence parallel to one pair of sides. What dimensions of the outer rectangle will minimize the amount of force used?
3 answers
Do you mean to minimize the amount of FENCE used? I don't see what force has to do with it. It also seeme to me that, by making the outer rectangle very narrow, the amount of fence required to divide it in half can be reduced to zero.
I assume you mean "fence" used.
Three cross fences of length w
area = w L = 384
so w = 384/L
total fence length= t = 3w + 2 L
t = 3*384/L + 2 L
t = 1152/L + 2 L
for min dt/dL = 0
dt/dL = 0 = -1152/L^2 + 2
2 L^2 = 1152
L^2 = 576
L = 24
then w = 16
Three cross fences of length w
area = w L = 384
so w = 384/L
total fence length= t = 3w + 2 L
t = 3*384/L + 2 L
t = 1152/L + 2 L
for min dt/dL = 0
dt/dL = 0 = -1152/L^2 + 2
2 L^2 = 1152
L^2 = 576
L = 24
then w = 16
I misread the problem, and forgot that the fence had to also enclose the outer perimter, which was clearly stated.
1 answer