A campground owner plans to enclose a rectangular field adjacent to a river. The owner wants the field to contain 125,000 square meters. No fencing is required along the river. What dimensions (in meters) will use the least amount of fencing

The dimensions (in meters) that  will use the least amount of fencing is 500m ; 250m

Let the   sides represent L and W

Where:

L=Length

W=Width

First step

LW = 125,000 square meters

W = 125,000/L

Second step is to determine the perimeter

Perimeter= 2L + 2W

Perimeter= 2L + 125,000/L

Third step is for us to set  the derivative to zero and then determine L

Perimeter = 2 - 250,000/L^2 = 0

2L^2 = 500,000

L^2=500,000/2

L^2 = 250,000

L = √(250,0000

L = 500 m

Fourth step is to  determine W

W= 125,000/500

W= 250 m

Inconclusion The dimensions (in meters) that  will use the least amount of fencing is 500m ; 250m  

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Step-by-step explanation:

Let us assume the length of the field = x meters

Let us assume the breadth if the field = y meters

Now, let us assume the one length and twice the width.

So, the length of the total fencing = x + y + y  = (x + 2 y) meters

Also, area of the field  = Length x Breadth  

                                      = (x meters )( y meters) =x y sq m = 1,25,000 sq m

⇒ x y   =  1,25,000

or,

Putting this value in (x + 2 y), we get:

P =  (x + 2 y) =

Now,    for minimizing the fencing perimeter.

On solving , we get:

So, the width of the perimeter = y = 250 meters

Hence, the needed length of the fencing is 500 m.

and the needed width of the fencing is 250 m.

15% chance.

step-by-step explanation:

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care to share were the trapezoid shown is ?