Please help 100 points!! 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.

Step-by-step explanation:

The volume of a rectangular prism is given by the formula

V = lwh

where V = volume, l = length, w = width, and h = height.

Therefore, dimensions of the box are 3 ft, 2 ft and 12 ft.

Dimensions:

Length = 3 feet

Width = 2 feet

Height = 12 feet

Step-by-step explanation:

72 = length × width × height

72 = x(x-1)(x+9)

72 = x(x²-x+9x-9)

72 = x³ + 8x² - 9x

x³ + 8x² - 9x - 72 = 0

x = 3, -3, -8

Can be obtained using factor theorem. Just try factors of 72 for 0.

Since x is the length, can't be negative.

So x = 3

x - 1 = 2

x + 9 = 12

Dimensions:

Length = 3 feet

Width = 2 feet

Height = 12 feet

22 dimes and 9 nickels

step-by-step explanation: