An open-topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard that has dimensions of 20cm by 30cm and folding up the sides. Determine the dimensions of the squares that must be cut to create a box with a volume of 1008cm^3.

Question

An open-topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard that has dimensions of 20cm by 30cm and folding up the sides. Determine the dimensions of the squares that must be cut to create a box with a volume of 1008cm^3. 
length=30-2x
width=20-2x
h=x
I don't get this because x and cm aren't interchangeable digits.

Steve · Accepted Answer

no idea what your complaint is about. x is a variable, and its units are cm. Multiply the three expressions and you get cm^3.

x(20-2x)(30-2x) = 1008
4x^3 - 100x^2 + 600x - 1008 = 0
scale down by 4:
x^3 - 25x^2 + 150x - 252 = 0

252 = 2*2*3*3*7
The only integer root is x=3, so the required box is

3×14×24 = 1008

sulaimon · Answer

Actual length = 23•8m 1cm to 2m

rasim · Answer

Why is it always (whatever number -2x)? why the -2x?