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A 384 square meter plot of land ts to be enclosed by a fence and divided into two equal parts by another fence parallel to one pair sides. What dimensions of the outer rectangle will minimize the amount of fence used?

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Mohammed R. | Specialist in GED and College Prep MathSpecialist in GED and College Prep Math
11
Let,
     Length of rectangle = l
     Width of rectangle = w
     Total length of fence = x
So, l*w = 384
     w = 384/l..........(1)
As the area must be divided by a fence parallel to the 2 shortest sides, let the shortest side be w and the longest be l
x = 3l + 2w
   = 3l + 768/[Plug in w from (1)]
Take the derivative,
x' = 3-768/l2
Taking x' = 0,
3-768/l= 0
3 = 768/l
3*l2 = 768
l2 = 256 
l = 16
Plug l into equation (1) and solve for w,
w = 384/16
   = 24
Hence, an outer rectangle of 16m*24m will minimize the amount of fence used