Liana has 800 yards of fencing to enclose a rectangular area. How do you maximize the area?

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Liana has 800 yards of fencing to enclose a rectangular area. How do you maximize the area?

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Answer 1 · 2016-02-19T12:54:20

Area can be maximized by fencing a square of side $200$ yards.

Explanation:

Given perimeter of a rectangle, square has the maximum area (proof given below).

Let $x$ be one of the side and $a$ be te perimeter then the other side would be $a/2-x$ and area would be $x(a/2-x)$ or $-x^2+ax/2$ . The function will be zero when first derivative of the function is equal to zero and second derivative is negative,

As first derivative is $-2x+a/2$ and this will be zero, when $-2x+a/2=0$ or $x=a/4$ . Note that second derivative is $-2$ . Then two sides will be $a/4$ each that the it would be square.

Hence if perimeter is 800 yards and it is a square, one side would be $800/4=200$ yards.

Hence area can be maximized by fencing a square of side $200$ yards.

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Liana has 800 yards of fencing to enclose a rectangular area. How do you maximize the area?

1 Answer

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