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A rancher has 600 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 toone of the field's shorter sides. Find the dimensions that maximize the enclosed area. Write your answers as fractions reduced to lowest terms.KeypadAnswer

Question
A rancher has 600 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.
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A rancher has 600 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. Keypad Answer

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Step 1

Consider the length of shorter side is x feet.

Then the length of longer side is

Зx
600- Зх 300-
2
2
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Зx 600- Зх 300- 2 2

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Step 2

Now find the area of the rectangular field as follows.

3x
A x300
2
3.x2
=300x
2
and b 300
2
Here a
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3x A x300 2 3.x2 =300x 2 and b 300 2 Here a

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Step 3

For maximum value is calc...

-b
х%3
2a
-300
-3
2
2
300
3
= 100
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-b х%3 2a -300 -3 2 2 300 3 = 100

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