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Viktor [21]
3 years ago
13

Peter has 3200 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed a

rea. What is the maximum​ area?
Mathematics
2 answers:
salantis [7]3 years ago
8 0

Answer:

A = 640000\,yd^{2}

Step-by-step explanation:

Expression for the rectangular area and perimeter are, respectively:

A (x,y) = x\cdot y

3200\,yd = 2\cdot (x+y)

After some algebraic manipulation, area expression can be reduce to an one-variable form:

y = 1600 -x

A (x) = x\cdot (1600-x)

The first derivative of the previous equation is:

\frac{dA}{dx}= 1600-2\cdot x

Let the expression be equalized to zero:

1600-2\cdot x=0

x = 800

The second derivative is:

\frac{d^{2}A}{dx^{2}} = -2

According to the Second Derivative Test, the critical value found in previous steps is a maximum. Then:

y = 800

The maximum area is:

A = (800\,yd)\cdot (800\,yd)

A = 640000\,yd^{2}

Aleonysh [2.5K]3 years ago
6 0

Answer:

74/4= 18.5

Step-by-step explanation:

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