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worty [1.4K]
2 years ago
8

An ottoman shaped like a rectangular prism has a length of x, a width two inches shorter than the length, and a height two inche

s taller than the length. Enter the function that represents the volume, V, then find the length, width, and height of the ottoman if the volume is 5,760 in3.
Mathematics
1 answer:
larisa [96]2 years ago
8 0

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

<h3></h3><h3></h3><h3>Volume of a rectangular prism</h3>
  • v = lwh

where

l = length

w = width

h = height

Therefore,

The length is as follows:

  • l = x

The width two inches shorter than the length:

  • w = x - 2

The height two inches taller than the length:

  • h = x + 2

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

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