Question

A box in the shape of a rectangular prism has a volume of 96 cubic feet. The box has a length of (x+8) feet, a width of x feet, and a height of (x-2) feet. Find the dimensions of the box.the length is __ feet, the width is __ feet, and the height is __ feetshow work please

Answer 1

The length is 12 ft, the width is 4 ft and the height is 2 ft

Step-by-step explanation:

Here, we want to get the values of the dimensions of the box

The volume is simply the product of the length, width, and height

We have that as follows:

`\begin{gathered} (x+8)(x)(x-2)\text{ = }96 \\ x(x^2+6x-16)=96 \\ x^3+6x^2-16x\text{ = 96} \end{gathered}`

By plotting the function, we have 3 intercepts on the x-axis as shown below:

These intercepts are the solutions to the equation. We have the values as:

x = -6, x = -4 and x = 4

x cannot be -6 and -4 as dimension cannot be negative

Thus, we are left with 4

The side lengths are thus:

4 ft, (4+8) ft and (4-2) ft

These are 4 ft, 12 ft and 2 ft