Math, asked by austincorreia22, 7 months ago

A rancher has 400 feet of fencing to put around a rectangular field and then subdivide the field into 2 identical smaller rectangular plots by placing a fence parallel to one of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms.

Answers

Answered by hanshu1234
0

Step-by-step explanation:

Let L be the length of rectangular field, and W its width.

After the division we got 4 W's (2 for entire field, and 2 for subdivision) and 2 L's, that is:

 

2L+4W=400  , Let A be the area of the field (A=WL), then

 

2A+4W2=400W

A=200W-2W2

dA/dW = 200-4W

equalize it to zero - to find the extremum; we'll find W=50

Correspondingly, L=(400-4*50)/2=100

 

So, dimensions that maximize the are for given geometry(including fence's length) would be 100 by 50.

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