Answer:
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=[tex]l\times b\times h[/tex]
Box is in cuboid shaped
Therefore, volume of box=[tex]6(x-12)(x-12)[/tex]
[tex]6(x^2-24x+144)=864[/tex]
[tex]x^2-24x+144=\frac{864}{6}[/tex]
[tex]x^2-24x+144=144[/tex]
[tex]x^2-24x+144-144=0[/tex]
[tex]x(x-24)=0[/tex]
Then ,[tex]x=0 , x-24=0[/tex]
[tex]x=24[/tex]
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
