# The width of a box is 2meters less than the length. The height is 1meter less than the length. The volume is 60 cu. meters. Find the length of the box?

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by mjd1

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by mjd1

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L*ength ⇒ 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:

a*x² + 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*

* is an imaginary number*

Therefore the roots (x) are:

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*

By Completing the square:

a

Therefore the roots (x) are:

Choose the positive number 5. The dimensions are:

Length, x ⇒

To check:

(5 meters) × (3 meters) × (4 meters) = 60 cubic meters