Answer:
Width = 24 inches
Length = 40 inches
Step-by-step explanation:
Let the width of the original piece of metal = [tex]x[/tex] inches
As per question,
Length of the original piece of metal = [tex]2x-8[/tex] inches
Square boxes of each side 4 inches is cut from each corner.
Therefore, height of the box = 4 inches
Width of the box = [tex]x-8[/tex] inches
Length of the box = [tex]2x-16[/tex] inches
Volume of a cuboid is given as:
[tex]Volume = Length \times Width \times Height[/tex]
Putting all the values:
[tex]2048 = 4 (x-8)(2x-16)\\\Rightarrow 256 = (x-8)^2\\\Rightarrow 16 = x-8\\\Rightarrow x =24\ inches[/tex]
Therefore, the width of original piece of metal = 24 inches
The length of original piece of metal = 2 [tex]\times[/tex] 24 - 8 = 40 inches
