creek

The back of Dante's property is a creek. Dante would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a corral. If there is 760 feet of fencing available, what is the maximum possible area of the corral?

Hello sandwich!

$A= a\cdot b\\ a+2b=760\ ft\\ 2b=760\ ft-a\\ b=380\ ft-\frac{a}{2}$

$A=f(a)=a\cdot (380\ ft-\frac{a}{2})\\ A=f(a)=-\frac{a^2}{2}+380\ ft\cdot a\\ A'= \frac{df(a)}{da}=-a+380\ ft=0$

$\color{blue}a=380\ ft\\ b=380\ ft-\frac{a}{2}=380\ ft-190\ ft\\ \color{blue}b=190\ ft$

Dante creates a rectangular field 380ft * 190ft.

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