Question 249053: well i have to do these work sheet worth alot of points and its confusing heres wat it says..
task description
the chief designer of the company has retired and names you as his replacement. this is your big chance to design the new garden area for wal-mart: your promotion depends on your success. you need to develop a team of architects, by adding two more people. the CEO eoulf likr you to create a model as well as complete and show the algebraic walkway together. each team member needs to keep a bi-weekly log of accomplishments,difficulties personal feelings you encounters while on the job. the logbook needs to be dated and sign for each entry and placed in order by dates.
the measurements we were giving but unfortunately, the fax was a little ruined when we received it. you will be creating a rectangular garden. which appears to be 4 feet longer than it is wide. it needs to be surrounded by a paved walkway 3 feet wide. a diagram has been created as accurately as possiable, given the fax was not clear. the last thing that was legible is the total area of the walkway is 432 square feet.
so the drawing is a big rectangle and theres a smaller one in the middle so basicly the big rectangle is the walkway and the one in the middle is the garden. so the paved walk way is 3 feet wide on all the sides ,but in the middle of the small rectangle on the side which is the width has a (X) and at the bottom which is the length it has x+4.
i need to find wat X is for both and the
(actual measurements:) width length area and perimeter)
(perimeter formula:) verbal model labels and algebraic models)
(area formula:) verbal model and labels and algebraic models)
all that is for the walkway.
and for the garden is the same thing but i dont understand how it goes and its confusing. please help me.
Found 3 solutions by scott8148, ankor@dixie-net.com, oberobic:
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! garden area + walkway area = overall area ___ x (x + 4) + 432 = (x + 6) (x + 10)
x^2 + 4x + 432 = x^2 + 16x + 160
272 = 12x ___ 22 2/3 = x
with this value, you can find all the others
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! This problem as I see it:
the garden dimensions are: L = (x+4); W = x
The walkway is 3' wide around the entire garden
The area of the walkway DISABLED_event_only= 432 sq/ft
:
area of the garden (A = L*W):
A = x(x+4) = x^2 + 4x sq ft
:
One thing to remember a 3' walkway adds 6' to the length and the width of the garden, hence:
Overall dimensions (garden and walkway):
L: (x+4) + 6 = (x+10)
W: (x+6)
It's area
(x+10)*(x+6) = x^2 + 16x + 60 sq/ft
:
The problem:
Overall area - garden area = walkway area (given as 432 sq/ft)
(x^2 + 16x + 60) - (x^2 + 4x) = 432
Remove brackets
x^2 + 16x + 60 - x^2 - 4x = 432
:
x^2 - x^2 + 16x - 4x = 432 - 60
:
12x = 372
x = 
x = 31 ft; is the width of the garden
and
31 + 4 = 35 ft; is the length of the garden
:
Find the overall dimension includes the walkway
35 + 6 = 41 ft, the length
31 + 6 = 37 ft, the width
:
:
Check our solution, find the area of both
(41*37) - (35*31) =
1517 - 1085 = 432; which the area of the walkway
:
:
You can find the perimeter and all that other stuff now.
Answer by oberobic(2304)  (Show Source):
You can put this solution on YOUR website! rectangular garden. 4 feet longer than it is wide.
surrounded by a paved walkway 3 feet wide
the total area of the walkway is 432 square feet.
.
Garden facts:
.
Outside Dimensions of Walkway
Add six because the walkway is 3 ft wide on both ends.
.
The area of the walkway is 432, but you have to subtract the area of the garden.
.
.
Substitute for Lw and Ww
.
Multiply these
.
Collect terms
.
Divide both sides by 12
.
Simplify
.
Recall Lg = Wg + 4
.
The outside dimensions of the garden are the inside dimensions of the walkway:
.
The outside dimensions of the walkway are
.
Check the answer to ensure the area of the walkway is 432.
.
Garden:
.
Rectangle defined by the outside dimensions of walkway
.
Subtract the area of the garden to determine the area of the walkway
.
Done as an area problem.
.
Now let's look at a perimeter problem solution.
.
Looking at the basic facts as a perimeter problem, the walkway is 432 sq ft and we know it is 3 ft wide,
However, we have to visual how the walkway is fitted around the garden rectangle. It is best to draw a figure and label all the parts. You'll notice the walkway appears to follow the perimeter, which in fact it does.
BUT
The walkway also fills in the corners where the perimeter is only a right-angle point. In a sense, there is no length to add to the perimeter at the corner. There are 4 of these corners, each of which has to be 3x3 feet. So this amounts to 9*4 = 36 sq ft. That means that of the total 432 sq ft of walkway, only 396 sq ft align with a side of the rectangle. The rest is in the corners.
.
Recall that the perimeter (P) of a rectangle is:
P = 2(L+W) = 2L + 2W
.
Since the walkway beside the perimeter is 396 sq ft, and it is 3 ft wide, we can determine P by dividing 396 by 3.
.
To work with smaller numbers, we can redefine the perimeter equation by dividing by 2:
.
Thus we know the L+W = 66
.
.
Substituting W+4 for L:
.
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Collecting terms and subtracting 4 from both sides
.
Divide both sides by 2 to eliminate the coefficient on W
.
Substituting back into the equation for L
.
Of course. the answer is the same as above, so this is another check.
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