A gift bag is shaped like a rectangular prism and has a volume of 1152 cubic inches. The width of the bag is w, the length is 2w+4, and the height of the bag is 18-w (which is greater than the width). What are the dimensions of the bag?

1. You must use the formula for calculate the volume of a rectangular prism, which is:

V = (h) (l) (w)

V: It is the volumen of the rectangular prism (V=1152 inches³).

h: It is the height of the rectangular prism (h=18-w).

l:It is the lenght of the rectangular prism (l=2w+4).

2. When you substitute these calues into the formula, you obtain:

V = (h) (l) (w)

1152 = (18-w) (2w+4) (w)

(18-w) (2w+4) (w) - 1152=0

3. Then, you should mutiply them:

36w²-2w³+72w-4w²-1152=0

32w²-2w³+72w-1152=0

4. When you factor, you obtain:

2 (w-16) (w-6) (w+6)

w1=16

w2=6

w3=-6

5. The problem says that the height is greater than the width, therefore, the widht is:

w=6 inches

6. The length is:

l=2w+4

l=2 (6) + 4

l=16 inches

7. And the height is:

h=18-w

h=18-6

h=12 inches

What are the dimensions of the bag?

The dimensions of the bag are:

l=16 inches

h=12 inches

w=6 inches