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A gift bag shaped like a rectangular prism has a volume of 1152 cubic inches. The dimensions of the gift bag in terms of its width are shown. The height is greater than the width. What are the dimensions of the gift bag? length: in., width: in., height: in.

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JcAlmighty
The answer is
w = 6 in
l = 16 in
h = 12 in

The volume of a rectangular prism with length l, width w, and height h is:
V = l * w * h

V = 1152 in³

After some internet research, I found out that:
l = 2w + 4
h = 18 - w

So,
V = l * w * h
1152 = (2w + 4) * w * (18 - w)

Multiply the first two factors:
1152 = (2w² + 4w) * (18 - w)

Multiply two remaining factors:
1152 = 36w² + 72w - 2 w³ - 4w²

Rearrange:
-2w³ + 36w² - 4w² + 72w = 1152
-2w³ + 32w² + 72w = 1152
-2w³ + 32w² + 72w - 1152 = 0

Divide all by 2:
-w³ + 16w² + 36w - 576 = 0

Multiply by (-1):
w³ - 16w² - 36w + 576 = 0

Rearrange:
(w³ - 36w) - (16w² - 576) = 0

Factor:
w * w² - w * 36 - (16 * w² - 16 * 36) = 0
w(w² - 36) - 16(w² - 36) = 0
(w - 16)(w² - 36) = 0
(w - 16)(w² - 6²) = 0
(w - 16)(w - 6)(w + 6) = 0

So, w - 16 = 0, or w - 6 = 0, or w + 6 = 0.
In other words: w = 16, or w = 6, or w = -6.

Width cannot be negative, so w ≠ -6.
If w = 16, then l = 2 * 16 + 4 = 32 + 4 = 36 and h = 18 - 16 = 2
But, since the height must be greater than the width (h > w), w ≠ 16

If w = 6, then l = 2 * 6 + 4 = 12 + 4 = 16 and h = 18 - 6 = 12.
Thus:
w = 6 in
l = 16 in
h = 12 in
aksnkj

The length of the bag is 48in, the width of the bag is 24in and the height of the bag is 48in.

Ractangular prism has 4 sides on its base. The volume of the rectangular is the product of the length of the base, the width of the base, and its height.

Let v be the volume of the prism and l, b and h be the length of the base, the width of the base, and its height respectively. Now volume can be formulated as,

[tex]v=l\times w\times h[/tex]

As the dimetions of the gift bag are not given so assume a regular gift bag with a length twice the width and height is equal to its length. therefore

[tex]l=2w[/tex]

[tex]\dfrac{I}{2} =w[/tex]

and

[tex]l=h[/tex]

Put the value of width and height in the formula of volume, we get,

[tex]v=l\times \dfrac{l}{2} \times l[/tex]

[tex]1152=\dfrac{l^3}{2}[/tex]

[tex]l^3=1152\times2[/tex]

[tex]l^3=3456[/tex]

[tex]l=\sqrt[3]{3456}[/tex]

[tex]l=48[/tex]

The length of the beg is 48 in. As the length is equal to height therefore height is also 48 in. the width is half of the length so the width is 24 in.

Hence, the length of the bag is 48in, the width of the bag is 24in and the height of the bag is 48in.

For more about the prism follow the link below-

https://brainly.com/question/318504

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