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.
suppose the length of the card board was x cm by x cm After squares of 4cm was cut from the corner, the dimension for the box will be: length=(x-8) cm width=(x-8) cm height=4 cm thus the volume will be: V=length*width*height V=4×(x-8)×(x-8)=144 x²-16x+64=36 this can be simplified to form a quadratic equation given by: x²-16x+28=0 solving the quadratic equation we get: x=2 or x=14 Thus we conclude that the original dimensions was: length=14 cm ; width=14 cm
