The original dimensions of the metal sheet are 22 inches by 52 inch
The volume is defined as the space occupied by any object in three dimensions. For a rectangular box, the volume will be calculated by multiplying the length, width, and height of the object.
If the Width of the metal = x
The length is 30 inches longer than its width= x+30
If Squares with sides 6 in long are cut from the four corners and the flaps are folded.
The length of the pre-folded box =x+30-12=(x+18)inch
The width of the pre-folded box = (x-6-6)inch = (x-12) inch
The height of the flap= 6 inch
The volume of the box = 2400-inch cubed
Volume of a Cuboid = LWH
6(x-12)(x+18)=2400
6x²+36x-1296=2400
6x²+36x-1296-2400=0
6x²+36x-3696=0
6(x-22)(28+x)=0
x-22=0 or x+28=0
Therefore the original dimensions of the metal sheet are 22 inches by 52 inch
The complete question with correct data is given below:-
A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 2400 incubatedwhat were the original dimensions of the piece of metal?
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