Question

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.

Answer 1

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