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Naddik [55]
2 years ago
11

Organizers of an outdoor concert will use 320 feet of fencing to fence off a rectangular vip section. What is the maximum area t

hat they can fence off
Mathematics
1 answer:
solong [7]2 years ago
8 0

<u>Answer-</u>

<em>The maximum area that they can fence off is</em><em> 6400 ft²</em>

<u>Solution-</u>

Organizers of an outdoor concert will use 320 feet of fencing to fence off a rectangular vip section.

i.e the perimeter of the rectangular section is 320 feet

Let us assume,

x = length of the rectangular section

y = breadth of the rectangular section

Hence,

\Rightarrow 2(x+y)=320\\\\\Rightarrow x+y=160\\\\\Rightarrow y=160-x

Now, we have to find the maximum area for which they can fence that off.

The area of the rectangular section is,

=x\cdot y

So we have to maximize the area function.

\Rightarrow f(x)=x\cdot y

Putting the value of y,

\Rightarrow f(x)=x\cdot (160-x)=160x-x^2

\Rightarrow f'(x)=160-2x

\Rightarrow f''(x)=-2

Finding the critical values,

\Rightarrow f'(x)=0

\Rightarrow 160-2x=0

\Rightarrow 2x=160

\Rightarrow x=80

∵ f"(x) is negative (i.e -2), so for the value of x=80, f(x) or area function will be maximum.

f(x)_{\text{at x=80}}=f(80)=160(80)-(80)^2=12800-6400=6400

Therefore, the maximum area that they can fence off is 6400 ft²

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