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?

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 = 3

*l*+ 2w = 3

*l*+ 768/*l*[Plug in w from (1)]Take the derivative,

x' = 3-768/

*l*^{2}Taking x' = 0,

3-768/

*l*^{2 }= 03 = 768/

3*

*l*^{2 }3*

*l*^{2}= 768*l*^{2}= 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**