An open box is to be constructed from a square piece of sheet metal by removing a square of side 6 feet from each corner and turning up the edges. if the box is to hold 864 cubic feet, what should be the dimensions of the sheet metal?

24 feet

Step-by-step explanation:

We are given that an open box is to be constructed from a square piece of sheet metal by removing a square side 6 feet from each corner and turning up the edges.

We have to find the dimensions of the sheet metal

Let x feet be the side of square  metal sheet

Length of box=x-12 feet (because 6 feet removed from each corner)

Width of box=x-12 feet

Height of box=6 feet

Volume of box=864 cubic feet

We know that volume of cuboid=

Box is in cuboid shaped

Therefore, volume of box=

Then ,

x=0 is not possible because side of square  metal sheet can not be zero

Therefore, x=24

All sides of square metal sheet are equal.

Hence, side of square metal sheet =24 feet

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2