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)(x+8) feet, a width of xx feet, and a height of (x−2)(x−2) feet. find the dimensions of the box.

Answer 1

length of box = 12 ft

width of box = 4 ft

height of box = 2 ft

Step-by-step explanation:

The volume of the rectangular prism can be calculated as follows:

volume = length * width * height

Answer 2

Answer:
length of box = 12 ft
width of box = 4 ft
height of box = 2 ft

Step-by-step explanation:
The volume of the rectangular prism can be calculated as follows:
volume = length * width * height

We have:
volume = 96 ft³
length = x+8 ft
width = x ft
height = x-2 ft

Now, substitute with the givens in the above formula and solve for x as follows:
96 = x(x+8)(x-2)
96 = (x²+8x)(x-2)
96 = x³ - 2x² + 8x² - 16x
x³ + 6x² - 16x - 96 = 0
(x+6)(x+4)(x-4) = 0
This means that:
either x = -6 .............> rejected as no side length can be negative
or x = -4 ...................> rejected as no side can be negative
or x = 4 ....................> accepted

Now that we have solved for x, we can get the side lengths as follows:
length = x + 8 = 4 + 8 = 12 ft
width = x = 4 ft
height = x - 2 = 4 - 2 = 2 ft

Hope this helps :)