A rectangular box is to be made from a piece of cardboard 6 cm wide and 14 cm long by cutting out squares of the same size from the four corners and turning up the sides. If the volume of the box is to be 40 cm^3, what should the length of the side of the square to be cut out be?

Answer 1

base of box will be 6-2x by 14-2x , where 0 < x < 3

x(6-2x)(14-2x) = 40
x(2)(3-x)(2)(7-x) = 40
x(3-x)(7-x) = 10
x^3 - 10x^2 + 21x - 10 = 0
tried x = ±1, ±2, ±3
x = 2 worked
by synthetic division,
(x-2)(x^2 - 8x + 5) = 0
x = 2, the other roots are outside our restriction

the cut-out square should be 2 cm by 2 cm