A rectangular plot of farmland are finite on one facet by a watercourse and on the opposite 3 sides by a single-strand electrical fence. With 800 m of wire at your disposal, what's the biggest space you'll be able to enclose, and what area unit its dimensions?

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A rectangular plot of farmland are finite on one facet by a watercourse and on the opposite 3 sides by a single-strand electrical fence. With 800 m of wire at your disposal, what&#039;s the biggest space you&#039;ll be able to enclose, and what area unit its dimensions?

Tionant · Accepted Answer

Let the sides of the rectangle-shaped fence be a and b.We only need to use wire for the three sides of the fence because the watercourse borders the farmland on one side. We possessa+b⋅2=800The area A of the farmland is given by:A=a⋅bUsing the first equation, we can write A as a function of b:A=A(b)=(800−2⋅b)⋅b=800b−2b2We want to maximize A.First we need&amp;nbsp;A′=800−4bwhich means that the points of extrema are:A′=0⇒b=200&amp;nbsp;mThe length of the other side isa=800−2⋅200=400&amp;nbsp;m&amp;nbsp;and the largest area is&amp;nbsp;A=400⋅200=80000&amp;nbsp;m2

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A rectangular plot of farmland will be bounded on one side by a river and on the

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