What is the largest area that can be fenced off of a rectangular garden if it will be fenced off with 220 feet of available material?

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What is the largest area that can be fenced off of a rectangular garden if it will be fenced off with 220 feet of available material?

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Answer 1 · 2015-02-25T22:39:43

It will be a square garden.

Let's do the maths:

Let's call the dimensions of the garden $x$ $x$ and $y$ $y$
Then we can immediately get rid of $y$ $y$ because the circumference of the fence is $220 f t$ $220ft$ , so:

$2 x + 2 y = 220 \to 2 y = 220 - 2 x \to y = 110 - x$ $2x+2y=220->2y=220-2x->y=110-x$

Now we come to area $A$ $A$ (substituting $y$ $y$ )

$A = x \cdot y = x (110 - x) = 110 x - x^{2}$ $A=x*y=x(110-x)=110x-x^2$

To find the maximum we set the derivative to $0$ $0$

$A'=110-2x=0->x=55->y=110-55=55$
(see earlier equation)

Answer : Area $A=55*55=3025 ft^2$

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What is the largest area that can be fenced off of a rectangular garden if it will be fenced off with 220 feet of available material?

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