Question

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

Answer 1

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

Volume of a rectangular prism

• 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