Find the solutions for w​

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.

16, 6 and 12 inches.

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