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06.10.2019 •
Mathematics
Arancher 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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Ответ:
Step-by-step explanation:
There's the two widths, x.
There's the four lengths, y.
4y+2x=600
Also, A=xy.
x=300-2y
A=y*(300-2y)
dA/dy=0= y*(-2)+(300-2y)
-2y-2y+300=0
y=300/4=150/2=75
x=300-2y=300-150=150
Then the long side is 150ft, the short side is 75ft.
Check to make sure that the sum of the lengths is 600: 300+300=600
And the maximum area is 150*75 ft2
Ответ: