A box in the shape of a rectangular prism has a volume of 72 cubic feet. The box has a length of x feet, a width of (x − 1) feet, and a height of (x + 9) feet. Find the dimensions of the box.

Length => x => 3 feet

Width = (x - 1) => (3 - 1) = 2 feet

Height = (x + 9) => (3 + 9) = 12 feet

Volume = 3 * 2 * 12 = 72 feet³

Step-by-step explanation:

Given;

Volume of the rectangular prism = 72 ft³

Length of the box = x ft

width of the box = (x-1) ft

height of the box = (x+9) ft

Volume of rectangular prism = Length * Width * Height

72 =  x * (x-1) * (x+9)

72 − x(x−1)(x+9) = 0

−x³ − 8x² + 9x + 72 = 0

− (x+8) (x+3) (x−3) = 0

multiply both sides by -1

(x+8) (x+3) (x−3) = 0

Compare each part to zero

x + 8 = 0   ,    x + 3 = 0    ,   x - 3 = 0

x = -8        ,      x = -3       ,      x = 3

The value of x can only be positive considering that we are looking at an actual measurement.

Therefore, x = 3

Substitute for x in the given

Length => x => 3 feet

Width = (x - 1) => (3 - 1) = 2 feet

Height = (x + 9) => (3 + 9) = 12 feet

the answer is here: : )

: