Calculation:
(Length) (width) (height)
(2w+4) (w) (18-w) = 1152
(2w^2+4w) (18-w) = 1152
Distributive property:
36w^2 -2w^3+72w-4w^2 =1152
Remember to use FOIL method:
-2w^3 +32w^2+72w-1152 =0
Like terms:
-2(w^3-16w^2-36w+576) = 0
Factor it by 2:
w^3 -16w^2-36w+576 =0
Simplify:
w^2(w-16)-36(w-16) =0
(w^2-36) (w-16) = 0
w= -6,6,16
Width:
w = 6,16
Since width is 16, then the height should be less than the width (18-16=2)
Length of gift bag: 2(6)+4
=16 inches.
Width of the bag: 6
Height of the bag: 18-6
12 inches.
Answer: 16, 6 and 12 inches.
