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This doesn't really have to do with the Web 2.0 Calculator, I just need help.

 

In these questions in my math book, I am given a length of fence to be used for enclosing the greatest area of land possible. I have to use a quadratic equation to figure out the greatest area. How do I find the equation I am supposed to use, and how does this help me figure out the area?

 

Here is an example:

An athletic club has 225 feet of fencing to enclose a tennis court. What quadratic function can be used to find the maximum area of the tennis court? Find the maximum area and the lengths of the sides of the resulting fence.

My math book just threw these questions at me without teaching me how to do them.

Guest Oct 18, 2017
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5+0 Answers

 #1
avatar+78755 
+4

Let P  be the perimeter of the fence  = 225

 

And  ..... P  = 2 ( Width + Length)    .....so.....

 

225  =   2 (W+ L)       divide by 2 in both sides

 

225 / 2  = W + L        subtract W  from both sides and simplify

 

112.5 - W = L        (1)

 

And the area, A,  =  W * L

 

So

 

A = W * L     .....  sub (1)  for L

 

A  =  W * ( 112.5 - W)      simplify

 

A =  112.5W  - W^2   rewrite as

 

A =  -W^2 + 112.5W

 

We  have an "upside down" parabola and is the quadratic we need

 

The area will be maximized at the W  value of      -112.5 / [2 * -1]  =  56.25

 

And using (1), the Length will be  112.5 - W  =   112.5 - 56.25  =  56.25

 

So......the maximum area will be   (56.25) * (56.25)  =  3164.0625 sq ft.

 

Note that the area  is maximized when we have a square with a side of 56.25 ft.....!!!

 

 

 

cool cool cool

CPhill  Oct 18, 2017
edited by CPhill  Oct 18, 2017
edited by CPhill  Oct 18, 2017
 #2
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Thank you so much! I was stuck on how to do this for hours!

 

Although, at one point, you said subtract L and you subtracted W...

Guest Oct 18, 2017
 #3
avatar+78755 
0

Sorry....that was a typo....I'll fix it....!!!!

 

Glad I could help!!!

 

 

cool cool cool

CPhill  Oct 18, 2017
 #4
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Is it just a coincidence that 225/4 =56. 25 ?? Just curious.

Guest Oct 18, 2017
 #5
avatar+78755 
+1

Nice spot....!!!   ......It is not a coincindence......

 

The area will always be maximized when each side of a rectangle is equal.....thus, the rectangle is a square!!!.......and it is produced when each side =   Perimeter/ 4 

 

 

cool cool cool

CPhill  Oct 18, 2017

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