Length ⇒ x
Width ⇒ x -2
Height ⇒ x - 1
Volume = 60 cubic meters
Length × Width × Height = Volume
(x) (x-2) (x -1) = 60
x³ - 3x² + 2x = 60
x³ - 3x² + 2x - 60 = 0
(x - 5) (x² + 2x + 12) = 0
x - 5 = 0
x = 5
Solve the quadratic equation x² + 2x + 12 by either Completing the Square or Quadratic Formula:
By Completing the square:
ax² + bx + (b/2)² = c + (b/2)²
x² + 2x + (2/2)² = - 12 + (2/2)²
x² + 2x + 1 = -11 + 1
x² + 2x + 1 = -11
(x + 1) (x + 1) = -11
(x + 1 )² = -11
[tex] \sqrt{(x + 1) ^{2} } = \sqrt{-11} [/tex]
[tex] \sqrt{-11} [/tex] is an imaginary number
[tex] \sqrt{-11} =i \sqrt{11} [/tex]
[tex]x +1 - 1 = -1 +i \sqrt{11} [/tex]
[tex]x+1-1 = -1-i \sqrt{11} [/tex]
Therefore the roots (x) are:
[tex]x = 5
[/tex]
[tex]x = -1+i \sqrt{11} [/tex]
[tex]x =-1-i \sqrt{11} [/tex]
Choose the positive number 5. The dimensions are:
Length, x ⇒ 5 meters
Width, x - 2 ⇒ 5 - 2 = 3 meters
Height, x - 1 ⇒ 5 - 1 = 4 meters
To check:
(5 meters) × (3 meters) × (4 meters) = 60 cubic meters
60 cubic meters = 60 cubic meters
