Small squares with sides 4 cm were cut from each of the corners of a square piece of cardboard. then it was folded into an open-top box. find the original dimensions of the square piece of cardboard if the volume of this box is 144 cm3.

Let the length and width of the square board be x  cm, when 4 cm are cut of from the corner, the dimensions of the box will be:'
length=(x-8) cm
width=(x-8) cm
height=x cm
thus the volume will be:
4(x-8)(x-8)=144 
4(x^2-16x+64)=144
this can be written into:
x^2-16x^2+64=36
solving the above gives us:
x=2 or x=14
when x=2, the dimensions will be negative. Thus we take x=14 cm, the original dimensions are 14 cm by 14 cm