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12 February, 19:26

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?

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  1. 12 February, 19:49
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    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
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