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

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