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# creek

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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?

Feb 10, 2020

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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.

!

Feb 10, 2020
edited by asinus  Feb 10, 2020