Question

Arnold has been given a 6 foot by 6 foot sheet of cardboard to make an open box by cutting an equal size square from each corner, folding up the resulting flaps, and taping at the corners. Your task is to label dimensions on a sketch with same size variable cut from each corner.

Part II: How does each variable expression relate to the length, width, and height of the box when folded?

Answer 1

We already know that our square sheet of cardboard has sides of 6 foot length, and after cutting a square of side x from each one of the corners, the new length of our sides will be
`6-2x`. Now, once we fold the sides to create our box, both the length and the width are going to be equal to
`6-2x`; after all, we are creating of box out of a square. The height on the other hand will be one the sides that we cut to create our box; therefore, the height will be
`x`.
To summarize, after folding, we will have a box of height =
`x`, width=
`6-2x`, and length=
`6-2x`