The function that represents the volume is as follows:
V(x) = x³ - 4x
The length, width, and height of the ottoman if the volume is 5,760 in³ are as follows:
length = 18 inches
width = 18 - 2 = 16 inches
height = 18 + 2 = 20 inches
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Volume of a rectangular prism</h3>
where
l = length
w = width
h = height
Therefore,
The length is as follows:
The width two inches shorter than the length:
The height two inches taller than the length:
Therefore,
volume = x (x - 2)(x + 2)
volume = x(x² + 2x - 2x - 4)
volume = x(x² - 4)
volume = x³ - 4x
If the volume is 5760 in³, the length, height and width can be found as follows:
5760 = x³ - 4x
x³ - 4x - 5760 = 0
By trying a few value of x, x = 18.
Therefore,
length = 18 inches
width = 18 - 2 = 16 inches
height = 18 + 2 = 20 inches
learn more on rectangular prism here: brainly.com/question/1780277?referrer=searchResults
