Answer:
390 m (perpendicular to river) x 780 m (parallel to river)
Step-by-step explanation:
Let y be the length of the side parallel to the river, and let x be the length of the sides perpendicular to the river.
The total area and length of fence required are given by:
[tex]A=304,200=xy\\y=\frac{304,200}{x} \\L=2x+y[/tex]
Rewriting the length of fence as a function of only x:
[tex]L=2x+\frac{304,200}{x}[/tex]
The value of x for which the derivate of L(x) is zero is the length of x that uses the least amount of fencing:
[tex]L=2x+\frac{304,200}{x}\\\frac{dL}{dx}=2- \frac{304,200}{x^2}=0\\x^2=152,100\\x=390[/tex]
If x = 390 m, then:
[tex]y=\frac{304,200}{390}\\y=780[/tex]
The dimensions that will use the least amount of fencing are 390 m x 780 m
