Answer:
Length of the rectangular prism = 4 meters
But other possible values = (-5meters or - 9 meters)
Step-by-step explanation:
The volume of a rectangular prism = Length × Width × Height
From the question above,
Length = x meters
Width = x - 1 meters
Height = x + 11 meters
Volume of the Rectangular prism = 180 cubic meters
Hence,
(x) × (x - 1) × (x + 11) = 180
We expand the brackets
(x)(x - 1) (x + 11) = 180
x² - x(x + 11) = 180
x² (x + 11) - x(x + 11) = 180
x³ + 11x² - x² + 11x =180
x³ +10x² - 11x = 180
x³ + 10x² - 11x -180 = 0
The above is a polynomial
We solve this polynomial to find x
x³ + 10x² - 11x -180 = 0
(x - 4)(x + 5) (x + 9) = 0
x - 4 = 0
x = 4
x + 5 = 0
x = -5
x + 9 = 0
x = -9
We are asked to find the various values for the length hence,
From the above question, we are told that
Length = x meters
Therefore, the length of this rectangular prism = 4 meters or -5 meters or -9 meters.
