Answer:
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
