Problema Solution
The length of a box is 5 more than the width and the height is 2 less than the width. If the volume is
equal to 150 cubic feet, what are the measurements for each side.
Answer provided by our tutors
let
x = the length of the width, x>0
x + 5 = the length of the box
x - 2 = the height of the box
V = 150 ft^3 the volume
the volume of a box is: V = width*length*height
x(x + 5)(x - 2) = 150
x^3 + 3x^2 - 10x - 150 = 0
we notice that for x = 5 the x(x + 5)(x - 2) = 150 is true thus one solution is x = 5
x + 5 = 5 + 5 = 10 ft
x - 2 = 5 - 2 = 3 ft
the measurements for the box are: 5 ft, 10 ft and 3 ft.