Question 249053
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 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 = {{{372/12}}}
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.