Math word problem.....?

Question

Show your work!!!!!!!!

You have 600 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river, find the length and width of the plot that will maximize the area? What is the largest area that will be enclosed?

Answer 1

OK

600 = L + 2w
600 - 2w = L

So - we know that L times W = Area

w (600 - 2w) = A ; we want to max this
600 w - 2w^2 = A ; we still want to max this. Max is where the first derivative = 0

First derivative = 600 - 4w = 0
600 = 4w
150 = w

So max area will be when w = 150. If w =150 , then L = ?

L = 600 - 150 -150 = 300

300 x 150 = Max area
45,000 sq ft = Max Area

Hope that helps.
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Answer 2

This is a related rate problem.
The area of a fenced rect. plot is lengthxwidth or ...L x w.
If the width is along the river, w + 2L = 600 ft.
or w = 600 - 2 L
Then L (600-2L) = Area(L)
d(Area)/dL = 600 - 4 L
At max L, 4 L = 600 and L = 150 ft.
Then w = 300 ft and area = 150 x 300 = 45000 ft^2

Answer 3

Since it's rectangular, let's call each of the shorter sides x. Then the longer side will be (600 - 2x)

The area is the length times the width:

A = x(600 - 2x) = 600x - 2x^2

To find the maximum area, differentiate A with respect to x and set that equal to zero (the inflection point of the curve which is a maximum or minimum:

dA/dx = 600 -4x = 0

x = 150

i.e. each side will be 150 and the length will be 300

Note that the resulting area is 45,000

Answer 4

The people that gave the answer with each side to equal 200 are incorrect. That would equal 40,000 sq feet. (Area= length X width) 200 X 200 = 40,000. The correct answer is 2 sides are 150 feet and one side is 300 feet (300 X 150 = 45,000 sq feet)

Answer 5

600= L + 2W L=600-2W A=LW A=[600-2W]w=600W-2WW. This is a parabola and is highest at W=150. So the length is 300 with the sides 150 each

Answer 6

40000 square feet. For any given rectangular perimeter, a square holds the largest area. 200 feet of fence on each side.

Answer 7

There are 3 sides getting fenced... divide it by two (since one side is twice as long as the other--rectangle!) and then you get 300, then divide that by 2 to get the distances of the two short sides... you should get the short sides both equal 150 and the long one 300.

Answer 8

40000sqft?

600/3=200
x 200 =40000

Answer 9

p=2(l+w)
in this case, though
p=l+2w
u need the highest area.
a=l*w
p=600
a=pw-2w^2
a=600w-2w^2
the highest is therefore 40000 square feet, since for any given rectangle's perimeter, the square will always have the most area. the answer is
p=600
l=200
w=200
a=40000

Answer 10

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