Question

An open box is to be made from a rectangular piece of cardboard that measures 6 in. by 3 in., by cutting out squares of the same size from each corner and bending up the sides. Is it possible to cut the squares so that the volume of the box is 40 in.3? Find all real solutions of this equation to answer the question. (6 – 2x)(3 – 2x)x = 40

Answer 1

No. The only real solution is x = 4. It is not possible to cut squares of this size.

Answer 2

To get the solution, we first simply the equation:

(6 – 2x)(3 – 2x)x = 40

(6-2x)(3x-2x^2) = 40

18x-18x^2-4x^3-40 = 0

Using the solver function of the calculator, we compute for the values of x.

The answers given are:

x1=−5.61787

x2=0.55893+1.21146∗i

x3=0.55893−1.21146∗i

Since dimension cannot be negative nor imaginary, therefore it is not possible to make a box with 40in^3 volume.