SOLUTION: the width of a box is 2 feet less than the length, the height is 8 feet greater than the length. The box has a cubic volume of 96 cubic feet. What are the dimensions of the box?

Question 334034: the width of a box is 2 feet less than the length, the height is 8 feet greater than the length. The box has a cubic volume of 96 cubic feet. What are the dimensions of the box?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
the width of a box is 2 feet less than the length, the height is 8 feet greater than the length. The box has a cubic volume of 96 cubic feet. What are the dimensions of the box?
let length be x
width = x-2
height = x+8
..
volume = 96 cu.ft.
..
x(x-2)(x+8)= 96
x(x^2+6x-16)=96
x^3+6x^2-16x=96
x^3+6x^2-16x-96=0
x^2(x+6)-16(x+6)=0
(x+6)(x^2-16)=0
(x+6)(x-4)(x+4)=0
ignoring the negative value of x
x= 4 the length
width = 2
height = 12
CHECK
4*2*12 = 96 cu.ft

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