Question 410593
you are planning a rectangular garden.
 Its length is twice its width x. 
You want a walkway 2ft wide around the garden.
:
x = the width of the garden
then
2x = the length
and
x(2x) = 2x^2; is the area of the garden
;
a. Write an expression for the area of the garden and walk.
Area including the walk (a 2' walk all the way around, adds 4' to each dimension):
A = (2x + 4)(x + 4)
FOIL
A = 2x^2 + 8x + 4x + 16
A = 2x^2 + 12x + 16, overall area
:
B. Write an expression for the area of the walk only.
Overall area - garden area = walkway area
2x^2 + 12x + 16 - 2x^2 = Walkway area
Find the walkway area (A)
A = 2x^2 - 2x^2 + 12x + 16
A = 12x + 16, walkway area
:
c. You have enough gravel to cover 76ft^2 and want to use it all on the walk.
 How big should you make the garden?
:
Replace A in the above equation with 76, find x which will give the dimension of the garden
12x + 16 = 76
12x = 76 - 16
12x = 60
x = {{{60/12}}}
x = 5 ft is the width of the garden
2(5) = 10 ft is the length
:
:
See if that makes sense
(5+4)*(10+4) = 126 sq/ft overall area
Garden: 5*10 =  50 sq/ft
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Walkway area   76 sq/ft