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