Question

The dimensions in inches of a shipping box can be expressed as width x, length x+1, and height x-4. The volume is 84ft sq. Find the dimensions of the box in feet.
1,1,4
2,2,21
2,6,7
3,4,7

Answer 1

X * (x + 1) * (x -4) = 84
x^2 + x * (x -4) = 84
x^3 + x^2 -4x^2 -4x = 84
x^3 - 3x^2 -4x -84 = 0
Using the cubic equation calculator:
http://www.1728.org/cubic.htm
x = 6
width 6
length 7
height 2
 

Answer 2

The volume of a box is (width)(length)(height).  
V = W*L*H 
 Plug in all the information we have: 
 84 ft^3 (incorrectly written as ft sq in the question)
 84 ft^3 = (x)(x+1)(x-4) = (x)(x^2-3x-4) = x^3 - 3x^2 - 4x. 
 Next, think of the factors of 84. 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84. 
 The value is x = 6.
 (6)(6+1)(6-4) = (6)(7)(2) = 84