the width of the flowerbed is w.

the total width is 2w+4

the total length is 2w + 8

the total area is (2w+4)(2w+8) = 165

4w^2 + 16w + 8w + 32 = 165

4w^2 + 24w + 32 = 165

4w^2 + 24w - 133 = 0

(2w - 7 )(2w + 19 ) = 0

2w + 19 = 0

w = -19/2 <-- negative measures; disqualified

2w-7 = 0

w = 7/2 = 3 and 1/2 = 3.5

Total width is 2*3.5 + 4 = 7+4 = 11

Total length is 2*3.5 + 8 = 7+8 = 15

area is 11*15 = 165

the width of the flowerbed is 3 and 1/2 = 3.5